C73:C6 - GroupNames

class	1	2	3A	3B	6A	6B	73A	73B	73C	73D	73E	73F	73G	73H	73I	73J	73K	73L
size	1	73	73	73	73	73	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	trivial
ρ₂	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	ζ₆	ζ₆⁵	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 6
ρ₄	1	-1	ζ₃	ζ₃²	ζ₆⁵	ζ₆	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 6
ρ₅	1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 3
ρ₆	1	1	ζ₃	ζ₃²	ζ₃	ζ₃²	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 3
ρ₇	6	0	0	0	0	0	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	orthogonal faithful
ρ₈	6	0	0	0	0	0	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	orthogonal faithful
ρ₉	6	0	0	0	0	0	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	orthogonal faithful
ρ₁₀	6	0	0	0	0	0	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	orthogonal faithful
ρ₁₁	6	0	0	0	0	0	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	orthogonal faithful
ρ₁₂	6	0	0	0	0	0	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	orthogonal faithful
ρ₁₃	6	0	0	0	0	0	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	orthogonal faithful
ρ₁₄	6	0	0	0	0	0	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	orthogonal faithful
ρ₁₅	6	0	0	0	0	0	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	orthogonal faithful
ρ₁₆	6	0	0	0	0	0	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	orthogonal faithful
ρ₁₇	6	0	0	0	0	0	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	orthogonal faithful
ρ₁₈	6	0	0	0	0	0	ζ₇₃⁶²+ζ₇₃⁵⁸+ζ₇₃⁴⁷+ζ₇₃²⁶+ζ₇₃¹⁵+ζ₇₃¹¹	ζ₇₃⁶⁷+ζ₇₃⁵⁴+ζ₇₃⁴⁸+ζ₇₃²⁵+ζ₇₃¹⁹+ζ₇₃⁶	ζ₇₃⁷²+ζ₇₃⁶⁵+ζ₇₃⁶⁴+ζ₇₃⁹+ζ₇₃⁸+ζ₇₃	ζ₇₃⁵²+ζ₇₃⁵¹+ζ₇₃⁴³+ζ₇₃³⁰+ζ₇₃²²+ζ₇₃²¹	ζ₇₃⁶⁹+ζ₇₃⁴¹+ζ₇₃³⁷+ζ₇₃³⁶+ζ₇₃³²+ζ₇₃⁴	ζ₇₃⁶¹+ζ₇₃⁵⁰+ζ₇₃³⁸+ζ₇₃³⁵+ζ₇₃²³+ζ₇₃¹²	ζ₇₃⁷¹+ζ₇₃⁵⁷+ζ₇₃⁵⁵+ζ₇₃¹⁸+ζ₇₃¹⁶+ζ₇₃²	ζ₇₃⁵⁹+ζ₇₃⁵³+ζ₇₃³⁹+ζ₇₃³⁴+ζ₇₃²⁰+ζ₇₃¹⁴	ζ₇₃⁶⁸+ζ₇₃⁴⁵+ζ₇₃⁴⁰+ζ₇₃³³+ζ₇₃²⁸+ζ₇₃⁵	ζ₇₃⁶⁰+ζ₇₃⁴⁴+ζ₇₃⁴²+ζ₇₃³¹+ζ₇₃²⁹+ζ₇₃¹³	ζ₇₃⁶⁶+ζ₇₃⁶³+ζ₇₃⁵⁶+ζ₇₃¹⁷+ζ₇₃¹⁰+ζ₇₃⁷	ζ₇₃⁷⁰+ζ₇₃⁴⁹+ζ₇₃⁴⁶+ζ₇₃²⁷+ζ₇₃²⁴+ζ₇₃³	orthogonal faithful

Smallest permutation representation of C₇₃⋊C₆
►On 73 points: primitive

Generators in S₇₃

(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)

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

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

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

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

Matrix representation of C₇₃⋊C₆ ►in GL₆(𝔽₄₃₉)

89	1	0	0	0	0
264	0	1	0	0	0
399	0	0	1	0	0
243	0	0	0	1	0
70	0	0	0	0	1
66	400	344	242	156	131

381	4	425	7	194	214
378	412	157	370	199	72
56	105	187	407	75	285
373	265	26	377	185	411
427	32	340	380	252	42
385	39	26	334	345	147

G:=sub<GL(6,GF(439))| [89,264,399,243,70,66,1,0,0,0,0,400,0,1,0,0,0,344,0,0,1,0,0,242,0,0,0,1,0,156,0,0,0,0,1,131],[381,378,56,373,427,385,4,412,105,265,32,39,425,157,187,26,340,26,7,370,407,377,380,334,194,199,75,185,252,345,214,72,285,411,42,147] >;

C₇₃⋊C₆ in GAP, Magma, Sage, TeX

C_{73}\rtimes C_6

% in TeX

G:=Group("C73:C6");

// GroupNames label

G:=SmallGroup(438,1);

// by ID

G=gap.SmallGroup(438,1);

# by ID

G:=PCGroup([3,-2,-3,-73,3890,221]);

// Polycyclic

G:=Group<a,b|a^73=b^6=1,b*a*b^-1=a^65>;

// generators/relations

Export

Subgroup lattice of C₇₃⋊C₆ in TeX
Character table of C₇₃⋊C₆ in TeX

381	4	425	7	194	214
378	412	157	370	199	72
56	105	187	407	75	285
373	265	26	377	185	411
427	32	340	380	252	42
385	39	26	334	345	147

381	4	425	7	194	214
378	412	157	370	199	72
56	105	187	407	75	285
373	265	26	377	185	411
427	32	340	380	252	42
385	39	26	334	345	147

G = C73⋊C6 order 438 = 2·3·73

The semidirect product of C73 and C6 acting faithfully

G = C₇₃⋊C₆ order 438 = 2·3·73

The semidirect product of C₇₃ and C₆ acting faithfully

381	4	425	7	194	214
378	412	157	370	199	72
56	105	187	407	75	285
373	265	26	377	185	411
427	32	340	380	252	42
385	39	26	334	345	147