C79:C6 - GroupNames

class	1	2	3A	3B	6A	6B	79A	79B	79C	79D	79E	79F	79G	79H	79I	79J	79K	79L	79M
size	1	79	79	79	79	79	6	6	6	6	6	6	6	6	6	6	6	6	6
ρ₁	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	trivial
ρ₂	1	-1	1	1	-1	-1	1	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 2
ρ₃	1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	1	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 3
ρ₄	1	-1	ζ₃²	ζ₃	ζ₆	ζ₆⁵	1	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 6
ρ₅	1	-1	ζ₃	ζ₃²	ζ₆⁵	ζ₆	1	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 6
ρ₆	1	1	ζ₃	ζ₃²	ζ₃	ζ₃²	1	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 3
ρ₇	6	0	0	0	0	0	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	orthogonal faithful
ρ₈	6	0	0	0	0	0	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	orthogonal faithful
ρ₉	6	0	0	0	0	0	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	orthogonal faithful
ρ₁₀	6	0	0	0	0	0	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	orthogonal faithful
ρ₁₁	6	0	0	0	0	0	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	orthogonal faithful
ρ₁₂	6	0	0	0	0	0	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	orthogonal faithful
ρ₁₃	6	0	0	0	0	0	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	orthogonal faithful
ρ₁₄	6	0	0	0	0	0	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	orthogonal faithful
ρ₁₅	6	0	0	0	0	0	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	orthogonal faithful
ρ₁₆	6	0	0	0	0	0	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	orthogonal faithful
ρ₁₇	6	0	0	0	0	0	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	orthogonal faithful
ρ₁₈	6	0	0	0	0	0	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	orthogonal faithful
ρ₁₉	6	0	0	0	0	0	ζ₇₉⁷⁵+ζ₇₉⁶⁶+ζ₇₉⁶²+ζ₇₉¹⁷+ζ₇₉¹³+ζ₇₉⁴	ζ₇₉⁷⁰+ζ₇₉⁵⁸+ζ₇₉⁴⁹+ζ₇₉³⁰+ζ₇₉²¹+ζ₇₉⁹	ζ₇₉⁷³+ζ₇₉⁶⁵+ζ₇₉⁵⁹+ζ₇₉²⁰+ζ₇₉¹⁴+ζ₇₉⁶	ζ₇₉⁶¹+ζ₇₉⁶⁰+ζ₇₉⁴²+ζ₇₉³⁷+ζ₇₉¹⁹+ζ₇₉¹⁸	ζ₇₉⁷¹+ζ₇₉⁵³+ζ₇₉⁴⁵+ζ₇₉³⁴+ζ₇₉²⁶+ζ₇₉⁸	ζ₇₉⁷⁶+ζ₇₉⁷²+ζ₇₉⁶⁹+ζ₇₉¹⁰+ζ₇₉⁷+ζ₇₉³	ζ₇₉⁶⁷+ζ₇₉⁵¹+ζ₇₉⁴⁰+ζ₇₉³⁹+ζ₇₉²⁸+ζ₇₉¹²	ζ₇₉⁷⁴+ζ₇₉⁴³+ζ₇₉⁴¹+ζ₇₉³⁸+ζ₇₉³⁶+ζ₇₉⁵	ζ₇₉⁶⁸+ζ₇₉⁶³+ζ₇₉⁵²+ζ₇₉²⁷+ζ₇₉¹⁶+ζ₇₉¹¹	ζ₇₉⁵⁷+ζ₇₉⁵⁴+ζ₇₉⁴⁷+ζ₇₉³²+ζ₇₉²⁵+ζ₇₉²²	ζ₇₉⁷⁷+ζ₇₉⁴⁸+ζ₇₉⁴⁶+ζ₇₉³³+ζ₇₉³¹+ζ₇₉²	ζ₇₉⁶⁴+ζ₇₉⁵⁰+ζ₇₉⁴⁴+ζ₇₉³⁵+ζ₇₉²⁹+ζ₇₉¹⁵	ζ₇₉⁷⁸+ζ₇₉⁵⁶+ζ₇₉⁵⁵+ζ₇₉²⁴+ζ₇₉²³+ζ₇₉	orthogonal faithful

Smallest permutation representation of C₇₉⋊C₆
►On 79 points: primitive

Generators in S₇₉

(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 72 73 74 75 76 77 78 79)

(2 25 24 79 56 57)(3 49 47 78 32 34)(4 73 70 77 8 11)(5 18 14 76 63 67)(6 42 37 75 39 44)(7 66 60 74 15 21)(9 35 27 72 46 54)(10 59 50 71 22 31)(12 28 17 69 53 64)(13 52 40 68 29 41)(16 45 30 65 36 51)(19 38 20 62 43 61)(23 55 33 58 26 48)

G:=sub<Sym(79)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79), (2,25,24,79,56,57)(3,49,47,78,32,34)(4,73,70,77,8,11)(5,18,14,76,63,67)(6,42,37,75,39,44)(7,66,60,74,15,21)(9,35,27,72,46,54)(10,59,50,71,22,31)(12,28,17,69,53,64)(13,52,40,68,29,41)(16,45,30,65,36,51)(19,38,20,62,43,61)(23,55,33,58,26,48)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79), (2,25,24,79,56,57)(3,49,47,78,32,34)(4,73,70,77,8,11)(5,18,14,76,63,67)(6,42,37,75,39,44)(7,66,60,74,15,21)(9,35,27,72,46,54)(10,59,50,71,22,31)(12,28,17,69,53,64)(13,52,40,68,29,41)(16,45,30,65,36,51)(19,38,20,62,43,61)(23,55,33,58,26,48) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79)], [(2,25,24,79,56,57),(3,49,47,78,32,34),(4,73,70,77,8,11),(5,18,14,76,63,67),(6,42,37,75,39,44),(7,66,60,74,15,21),(9,35,27,72,46,54),(10,59,50,71,22,31),(12,28,17,69,53,64),(13,52,40,68,29,41),(16,45,30,65,36,51),(19,38,20,62,43,61),(23,55,33,58,26,48)]])

Matrix representation of C₇₉⋊C₆ ►in GL₆(𝔽₁₄₂₃)

0	1	0	0	0	0
0	0	1	0	0	0
0	0	0	1	0	0
0	0	0	0	1	0
0	0	0	0	0	1
1422	886	63	1400	63	886

1	0	0	0	0	0
839	713	640	208	369	1075
473	595	92	545	1002	943
756	245	1322	175	72	1166
296	671	233	1146	342	261
1362	33	1125	747	301	100

G:=sub<GL(6,GF(1423))| [0,0,0,0,0,1422,1,0,0,0,0,886,0,1,0,0,0,63,0,0,1,0,0,1400,0,0,0,1,0,63,0,0,0,0,1,886],[1,839,473,756,296,1362,0,713,595,245,671,33,0,640,92,1322,233,1125,0,208,545,175,1146,747,0,369,1002,72,342,301,0,1075,943,1166,261,100] >;

C₇₉⋊C₆ in GAP, Magma, Sage, TeX

C_{79}\rtimes C_6

% in TeX

G:=Group("C79:C6");

// GroupNames label

G:=SmallGroup(474,1);

// by ID

G=gap.SmallGroup(474,1);

# by ID

G:=PCGroup([3,-2,-3,-79,4214,626]);

// Polycyclic

G:=Group<a,b|a^79=b^6=1,b*a*b^-1=a^56>;

// generators/relations

Export

Subgroup lattice of C₇₉⋊C₆ in TeX
Character table of C₇₉⋊C₆ in TeX

G = C79⋊C6 order 474 = 2·3·79

The semidirect product of C79 and C6 acting faithfully

G = C₇₉⋊C₆ order 474 = 2·3·79

The semidirect product of C₇₉ and C₆ acting faithfully