C71:C7 - GroupNames

class	1	7A	7B	7C	7D	7E	7F	71A	71B	71C	71D	71E	71F	71G	71H	71I	71J
size	1	71	71	71	71	71	71	7	7	7	7	7	7	7	7	7	7
ρ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	trivial
ρ₂	1	ζ₇⁴	ζ₇⁶	ζ₇²	ζ₇⁵	ζ₇	ζ₇³	1	1	1	1	1	1	1	1	1	1	linear of order 7
ρ₃	1	ζ₇²	ζ₇³	ζ₇	ζ₇⁶	ζ₇⁴	ζ₇⁵	1	1	1	1	1	1	1	1	1	1	linear of order 7
ρ₄	1	ζ₇³	ζ₇	ζ₇⁵	ζ₇²	ζ₇⁶	ζ₇⁴	1	1	1	1	1	1	1	1	1	1	linear of order 7
ρ₅	1	ζ₇⁶	ζ₇²	ζ₇³	ζ₇⁴	ζ₇⁵	ζ₇	1	1	1	1	1	1	1	1	1	1	linear of order 7
ρ₆	1	ζ₇⁵	ζ₇⁴	ζ₇⁶	ζ₇	ζ₇³	ζ₇²	1	1	1	1	1	1	1	1	1	1	linear of order 7
ρ₇	1	ζ₇	ζ₇⁵	ζ₇⁴	ζ₇³	ζ₇²	ζ₇⁶	1	1	1	1	1	1	1	1	1	1	linear of order 7
ρ₈	7	0	0	0	0	0	0	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	complex faithful
ρ₉	7	0	0	0	0	0	0	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	complex faithful
ρ₁₀	7	0	0	0	0	0	0	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	complex faithful
ρ₁₁	7	0	0	0	0	0	0	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	complex faithful
ρ₁₂	7	0	0	0	0	0	0	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	complex faithful
ρ₁₃	7	0	0	0	0	0	0	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	complex faithful
ρ₁₄	7	0	0	0	0	0	0	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	complex faithful
ρ₁₅	7	0	0	0	0	0	0	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	complex faithful
ρ₁₆	7	0	0	0	0	0	0	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	complex faithful
ρ₁₇	7	0	0	0	0	0	0	ζ₇₁⁷⁰+ζ₇₁⁵¹+ζ₇₁⁴¹+ζ₇₁³⁹+ζ₇₁³⁴+ζ₇₁²⁶+ζ₇₁²³	ζ₇₁⁶⁶+ζ₇₁⁶³+ζ₇₁⁵⁹+ζ₇₁⁵³+ζ₇₁⁴⁴+ζ₇₁⁴²+ζ₇₁²⁸	ζ₇₁⁶⁹+ζ₇₁⁶⁸+ζ₇₁⁵²+ζ₇₁⁴⁶+ζ₇₁³¹+ζ₇₁¹¹+ζ₇₁⁷	ζ₇₁⁶¹+ζ₇₁⁵⁶+ζ₇₁⁵⁵+ζ₇₁⁴⁷+ζ₇₁³⁵+ζ₇₁¹⁷+ζ₇₁¹³	ζ₇₁⁶⁴+ζ₇₁⁶⁰+ζ₇₁⁴⁰+ζ₇₁²⁵+ζ₇₁¹⁹+ζ₇₁³+ζ₇₁²	ζ₇₁⁵⁷+ζ₇₁⁵⁰+ζ₇₁⁴⁹+ζ₇₁³⁸+ζ₇₁⁹+ζ₇₁⁶+ζ₇₁⁴	ζ₇₁⁴³+ζ₇₁²⁹+ζ₇₁²⁷+ζ₇₁¹⁸+ζ₇₁¹²+ζ₇₁⁸+ζ₇₁⁵	ζ₇₁⁵⁸+ζ₇₁⁵⁴+ζ₇₁³⁶+ζ₇₁²⁴+ζ₇₁¹⁶+ζ₇₁¹⁵+ζ₇₁¹⁰	ζ₇₁⁶⁷+ζ₇₁⁶⁵+ζ₇₁⁶²+ζ₇₁³³+ζ₇₁²²+ζ₇₁²¹+ζ₇₁¹⁴	ζ₇₁⁴⁸+ζ₇₁⁴⁵+ζ₇₁³⁷+ζ₇₁³²+ζ₇₁³⁰+ζ₇₁²⁰+ζ₇₁	complex faithful

Smallest permutation representation of C₇₁⋊C₇
►On 71 points: primitive

Generators in S₇₁

(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71)

(2 46 38 33 21 49 31)(3 20 4 65 41 26 61)(5 39 7 58 10 51 50)(6 13 44 19 30 28 9)(8 32 47 12 70 53 69)(11 25 16 37 59 55 17)(14 18 56 62 48 57 36)(15 63 22 23 68 34 66)(24 42 71 27 35 40 52)(29 54 43 45 64 67 60)

G:=sub<Sym(71)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71), (2,46,38,33,21,49,31)(3,20,4,65,41,26,61)(5,39,7,58,10,51,50)(6,13,44,19,30,28,9)(8,32,47,12,70,53,69)(11,25,16,37,59,55,17)(14,18,56,62,48,57,36)(15,63,22,23,68,34,66)(24,42,71,27,35,40,52)(29,54,43,45,64,67,60)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71), (2,46,38,33,21,49,31)(3,20,4,65,41,26,61)(5,39,7,58,10,51,50)(6,13,44,19,30,28,9)(8,32,47,12,70,53,69)(11,25,16,37,59,55,17)(14,18,56,62,48,57,36)(15,63,22,23,68,34,66)(24,42,71,27,35,40,52)(29,54,43,45,64,67,60) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71)], [(2,46,38,33,21,49,31),(3,20,4,65,41,26,61),(5,39,7,58,10,51,50),(6,13,44,19,30,28,9),(8,32,47,12,70,53,69),(11,25,16,37,59,55,17),(14,18,56,62,48,57,36),(15,63,22,23,68,34,66),(24,42,71,27,35,40,52),(29,54,43,45,64,67,60)]])

Matrix representation of C₇₁⋊C₇ ►in GL₇(𝔽₆₉₅₉)

0	1	0	0	0	0	0
0	0	1	0	0	0	0
0	0	0	1	0	0	0
0	0	0	0	1	0	0
0	0	0	0	0	1	0
0	0	0	0	0	0	1
1	918	1422	1623	1011	4788	1992

1	0	0	0	0	0	0
1801	4396	2987	2575	4866	2466	2647
3677	897	2942	1850	3150	6355	3225
3172	6045	2076	6690	4614	1063	1445
3374	5673	686	4677	3044	2036	2980
1992	5399	1229	5462	4384	4877	6222
4245	1543	6585	3350	659	820	5886

G:=sub<GL(7,GF(6959))| [0,0,0,0,0,0,1,1,0,0,0,0,0,918,0,1,0,0,0,0,1422,0,0,1,0,0,0,1623,0,0,0,1,0,0,1011,0,0,0,0,1,0,4788,0,0,0,0,0,1,1992],[1,1801,3677,3172,3374,1992,4245,0,4396,897,6045,5673,5399,1543,0,2987,2942,2076,686,1229,6585,0,2575,1850,6690,4677,5462,3350,0,4866,3150,4614,3044,4384,659,0,2466,6355,1063,2036,4877,820,0,2647,3225,1445,2980,6222,5886] >;

C₇₁⋊C₇ in GAP, Magma, Sage, TeX

C_{71}\rtimes C_7

% in TeX

G:=Group("C71:C7");

// GroupNames label

G:=SmallGroup(497,1);

// by ID

G=gap.SmallGroup(497,1);

# by ID

G:=PCGroup([2,-7,-71,1261]);

// Polycyclic

G:=Group<a,b|a^71=b^7=1,b*a*b^-1=a^30>;

// generators/relations

Export

Subgroup lattice of C₇₁⋊C₇ in TeX
Character table of C₇₁⋊C₇ in TeX

G = C71⋊C7 order 497 = 7·71

The semidirect product of C71 and C7 acting faithfully

G = C₇₁⋊C₇ order 497 = 7·71

The semidirect product of C₇₁ and C₇ acting faithfully