D57:C3 - GroupNames

class	1	2	3A	3B	3C	3D	3E	6A	6B	19A	19B	19C	57A	57B	57C	57D	57E	57F
size	1	57	2	19	19	38	38	57	57	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	1	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₆⁵	ζ₆	1	1	1	1	1	1	1	1	1	linear of order 6
ρ₄	1	1	1	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃²	1	1	1	1	1	1	1	1	1	linear of order 3
ρ₅	1	-1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₆	ζ₆⁵	1	1	1	1	1	1	1	1	1	linear of order 6
ρ₆	1	1	1	ζ₃²	ζ₃	ζ₃²	ζ₃	ζ₃²	ζ₃	1	1	1	1	1	1	1	1	1	linear of order 3
ρ₇	2	0	-1	2	2	-1	-1	0	0	2	2	2	-1	-1	-1	-1	-1	-1	orthogonal lifted from S₃
ρ₈	2	0	-1	-1-√-3	-1+√-3	ζ₆	ζ₆⁵	0	0	2	2	2	-1	-1	-1	-1	-1	-1	complex lifted from C₃×S₃
ρ₉	2	0	-1	-1+√-3	-1-√-3	ζ₆⁵	ζ₆	0	0	2	2	2	-1	-1	-1	-1	-1	-1	complex lifted from C₃×S₃
ρ₁₀	6	0	6	0	0	0	0	0	0	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	orthogonal lifted from C₁₉⋊C₆
ρ₁₁	6	0	6	0	0	0	0	0	0	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	orthogonal lifted from C₁₉⋊C₆
ρ₁₂	6	0	6	0	0	0	0	0	0	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	orthogonal lifted from C₁₉⋊C₆
ρ₁₃	6	0	-3	0	0	0	0	0	0	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	-ζ₃ζ₁₉¹⁷-ζ₃ζ₁₉¹⁶+ζ₃ζ₁₉¹⁴-ζ₃ζ₁₉⁵+ζ₃ζ₁₉³+ζ₃ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	ζ₃ζ₁₉¹⁸+ζ₃ζ₁₉¹²-ζ₃ζ₁₉¹¹+ζ₃ζ₁₉⁸-ζ₃ζ₁₉⁷-ζ₃ζ₁₉-ζ₁₉¹¹-ζ₁₉⁷-ζ₁₉	-ζ₃²ζ₁₉¹⁷-ζ₃²ζ₁₉¹⁶+ζ₃²ζ₁₉¹⁴-ζ₃²ζ₁₉⁵+ζ₃²ζ₁₉³+ζ₃²ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	-ζ₃²ζ₁₉¹⁵-ζ₃²ζ₁₉¹³-ζ₃²ζ₁₉¹⁰+ζ₃²ζ₁₉⁹+ζ₃²ζ₁₉⁶+ζ₃²ζ₁₉⁴-ζ₁₉¹⁵-ζ₁₉¹³-ζ₁₉¹⁰	-ζ₃ζ₁₉¹⁸-ζ₃ζ₁₉¹²+ζ₃ζ₁₉¹¹-ζ₃ζ₁₉⁸+ζ₃ζ₁₉⁷+ζ₃ζ₁₉-ζ₁₉¹⁸-ζ₁₉¹²-ζ₁₉⁸	ζ₃²ζ₁₉¹⁵+ζ₃²ζ₁₉¹³+ζ₃²ζ₁₉¹⁰-ζ₃²ζ₁₉⁹-ζ₃²ζ₁₉⁶-ζ₃²ζ₁₉⁴-ζ₁₉⁹-ζ₁₉⁶-ζ₁₉⁴	orthogonal faithful
ρ₁₄	6	0	-3	0	0	0	0	0	0	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₃ζ₁₉¹⁸+ζ₃ζ₁₉¹²-ζ₃ζ₁₉¹¹+ζ₃ζ₁₉⁸-ζ₃ζ₁₉⁷-ζ₃ζ₁₉-ζ₁₉¹¹-ζ₁₉⁷-ζ₁₉	-ζ₃²ζ₁₉¹⁵-ζ₃²ζ₁₉¹³-ζ₃²ζ₁₉¹⁰+ζ₃²ζ₁₉⁹+ζ₃²ζ₁₉⁶+ζ₃²ζ₁₉⁴-ζ₁₉¹⁵-ζ₁₉¹³-ζ₁₉¹⁰	-ζ₃ζ₁₉¹⁸-ζ₃ζ₁₉¹²+ζ₃ζ₁₉¹¹-ζ₃ζ₁₉⁸+ζ₃ζ₁₉⁷+ζ₃ζ₁₉-ζ₁₉¹⁸-ζ₁₉¹²-ζ₁₉⁸	-ζ₃ζ₁₉¹⁷-ζ₃ζ₁₉¹⁶+ζ₃ζ₁₉¹⁴-ζ₃ζ₁₉⁵+ζ₃ζ₁₉³+ζ₃ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	ζ₃²ζ₁₉¹⁵+ζ₃²ζ₁₉¹³+ζ₃²ζ₁₉¹⁰-ζ₃²ζ₁₉⁹-ζ₃²ζ₁₉⁶-ζ₃²ζ₁₉⁴-ζ₁₉⁹-ζ₁₉⁶-ζ₁₉⁴	-ζ₃²ζ₁₉¹⁷-ζ₃²ζ₁₉¹⁶+ζ₃²ζ₁₉¹⁴-ζ₃²ζ₁₉⁵+ζ₃²ζ₁₉³+ζ₃²ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	orthogonal faithful
ρ₁₅	6	0	-3	0	0	0	0	0	0	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	-ζ₃²ζ₁₉¹⁷-ζ₃²ζ₁₉¹⁶+ζ₃²ζ₁₉¹⁴-ζ₃²ζ₁₉⁵+ζ₃²ζ₁₉³+ζ₃²ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	-ζ₃ζ₁₉¹⁸-ζ₃ζ₁₉¹²+ζ₃ζ₁₉¹¹-ζ₃ζ₁₉⁸+ζ₃ζ₁₉⁷+ζ₃ζ₁₉-ζ₁₉¹⁸-ζ₁₉¹²-ζ₁₉⁸	-ζ₃ζ₁₉¹⁷-ζ₃ζ₁₉¹⁶+ζ₃ζ₁₉¹⁴-ζ₃ζ₁₉⁵+ζ₃ζ₁₉³+ζ₃ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	ζ₃²ζ₁₉¹⁵+ζ₃²ζ₁₉¹³+ζ₃²ζ₁₉¹⁰-ζ₃²ζ₁₉⁹-ζ₃²ζ₁₉⁶-ζ₃²ζ₁₉⁴-ζ₁₉⁹-ζ₁₉⁶-ζ₁₉⁴	ζ₃ζ₁₉¹⁸+ζ₃ζ₁₉¹²-ζ₃ζ₁₉¹¹+ζ₃ζ₁₉⁸-ζ₃ζ₁₉⁷-ζ₃ζ₁₉-ζ₁₉¹¹-ζ₁₉⁷-ζ₁₉	-ζ₃²ζ₁₉¹⁵-ζ₃²ζ₁₉¹³-ζ₃²ζ₁₉¹⁰+ζ₃²ζ₁₉⁹+ζ₃²ζ₁₉⁶+ζ₃²ζ₁₉⁴-ζ₁₉¹⁵-ζ₁₉¹³-ζ₁₉¹⁰	orthogonal faithful
ρ₁₆	6	0	-3	0	0	0	0	0	0	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	-ζ₃²ζ₁₉¹⁵-ζ₃²ζ₁₉¹³-ζ₃²ζ₁₉¹⁰+ζ₃²ζ₁₉⁹+ζ₃²ζ₁₉⁶+ζ₃²ζ₁₉⁴-ζ₁₉¹⁵-ζ₁₉¹³-ζ₁₉¹⁰	-ζ₃ζ₁₉¹⁷-ζ₃ζ₁₉¹⁶+ζ₃ζ₁₉¹⁴-ζ₃ζ₁₉⁵+ζ₃ζ₁₉³+ζ₃ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	ζ₃²ζ₁₉¹⁵+ζ₃²ζ₁₉¹³+ζ₃²ζ₁₉¹⁰-ζ₃²ζ₁₉⁹-ζ₃²ζ₁₉⁶-ζ₃²ζ₁₉⁴-ζ₁₉⁹-ζ₁₉⁶-ζ₁₉⁴	ζ₃ζ₁₉¹⁸+ζ₃ζ₁₉¹²-ζ₃ζ₁₉¹¹+ζ₃ζ₁₉⁸-ζ₃ζ₁₉⁷-ζ₃ζ₁₉-ζ₁₉¹¹-ζ₁₉⁷-ζ₁₉	-ζ₃²ζ₁₉¹⁷-ζ₃²ζ₁₉¹⁶+ζ₃²ζ₁₉¹⁴-ζ₃²ζ₁₉⁵+ζ₃²ζ₁₉³+ζ₃²ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	-ζ₃ζ₁₉¹⁸-ζ₃ζ₁₉¹²+ζ₃ζ₁₉¹¹-ζ₃ζ₁₉⁸+ζ₃ζ₁₉⁷+ζ₃ζ₁₉-ζ₁₉¹⁸-ζ₁₉¹²-ζ₁₉⁸	orthogonal faithful
ρ₁₇	6	0	-3	0	0	0	0	0	0	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₃²ζ₁₉¹⁵+ζ₃²ζ₁₉¹³+ζ₃²ζ₁₉¹⁰-ζ₃²ζ₁₉⁹-ζ₃²ζ₁₉⁶-ζ₃²ζ₁₉⁴-ζ₁₉⁹-ζ₁₉⁶-ζ₁₉⁴	-ζ₃²ζ₁₉¹⁷-ζ₃²ζ₁₉¹⁶+ζ₃²ζ₁₉¹⁴-ζ₃²ζ₁₉⁵+ζ₃²ζ₁₉³+ζ₃²ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	-ζ₃²ζ₁₉¹⁵-ζ₃²ζ₁₉¹³-ζ₃²ζ₁₉¹⁰+ζ₃²ζ₁₉⁹+ζ₃²ζ₁₉⁶+ζ₃²ζ₁₉⁴-ζ₁₉¹⁵-ζ₁₉¹³-ζ₁₉¹⁰	-ζ₃ζ₁₉¹⁸-ζ₃ζ₁₉¹²+ζ₃ζ₁₉¹¹-ζ₃ζ₁₉⁸+ζ₃ζ₁₉⁷+ζ₃ζ₁₉-ζ₁₉¹⁸-ζ₁₉¹²-ζ₁₉⁸	-ζ₃ζ₁₉¹⁷-ζ₃ζ₁₉¹⁶+ζ₃ζ₁₉¹⁴-ζ₃ζ₁₉⁵+ζ₃ζ₁₉³+ζ₃ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	ζ₃ζ₁₉¹⁸+ζ₃ζ₁₉¹²-ζ₃ζ₁₉¹¹+ζ₃ζ₁₉⁸-ζ₃ζ₁₉⁷-ζ₃ζ₁₉-ζ₁₉¹¹-ζ₁₉⁷-ζ₁₉	orthogonal faithful
ρ₁₈	6	0	-3	0	0	0	0	0	0	ζ₁₉¹⁸+ζ₁₉¹²+ζ₁₉¹¹+ζ₁₉⁸+ζ₁₉⁷+ζ₁₉	ζ₁₉¹⁷+ζ₁₉¹⁶+ζ₁₉¹⁴+ζ₁₉⁵+ζ₁₉³+ζ₁₉²	ζ₁₉¹⁵+ζ₁₉¹³+ζ₁₉¹⁰+ζ₁₉⁹+ζ₁₉⁶+ζ₁₉⁴	-ζ₃ζ₁₉¹⁸-ζ₃ζ₁₉¹²+ζ₃ζ₁₉¹¹-ζ₃ζ₁₉⁸+ζ₃ζ₁₉⁷+ζ₃ζ₁₉-ζ₁₉¹⁸-ζ₁₉¹²-ζ₁₉⁸	ζ₃²ζ₁₉¹⁵+ζ₃²ζ₁₉¹³+ζ₃²ζ₁₉¹⁰-ζ₃²ζ₁₉⁹-ζ₃²ζ₁₉⁶-ζ₃²ζ₁₉⁴-ζ₁₉⁹-ζ₁₉⁶-ζ₁₉⁴	ζ₃ζ₁₉¹⁸+ζ₃ζ₁₉¹²-ζ₃ζ₁₉¹¹+ζ₃ζ₁₉⁸-ζ₃ζ₁₉⁷-ζ₃ζ₁₉-ζ₁₉¹¹-ζ₁₉⁷-ζ₁₉	-ζ₃²ζ₁₉¹⁷-ζ₃²ζ₁₉¹⁶+ζ₃²ζ₁₉¹⁴-ζ₃²ζ₁₉⁵+ζ₃²ζ₁₉³+ζ₃²ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	-ζ₃²ζ₁₉¹⁵-ζ₃²ζ₁₉¹³-ζ₃²ζ₁₉¹⁰+ζ₃²ζ₁₉⁹+ζ₃²ζ₁₉⁶+ζ₃²ζ₁₉⁴-ζ₁₉¹⁵-ζ₁₉¹³-ζ₁₉¹⁰	-ζ₃ζ₁₉¹⁷-ζ₃ζ₁₉¹⁶+ζ₃ζ₁₉¹⁴-ζ₃ζ₁₉⁵+ζ₃ζ₁₉³+ζ₃ζ₁₉²-ζ₁₉¹⁷-ζ₁₉¹⁶-ζ₁₉⁵	orthogonal faithful

Smallest permutation representation of D₅₇⋊C₃
►On 57 points

Generators in S₅₇

(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)

(1 57)(2 56)(3 55)(4 54)(5 53)(6 52)(7 51)(8 50)(9 49)(10 48)(11 47)(12 46)(13 45)(14 44)(15 43)(16 42)(17 41)(18 40)(19 39)(20 38)(21 37)(22 36)(23 35)(24 34)(25 33)(26 32)(27 31)(28 30)

(2 8 50)(3 15 42)(4 22 34)(5 29 26)(6 36 18)(7 43 10)(9 57 51)(11 14 35)(12 21 27)(13 28 19)(16 49 52)(17 56 44)(23 41 53)(24 48 45)(25 55 37)(30 33 54)(31 40 46)(32 47 38)

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

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), (1,57)(2,56)(3,55)(4,54)(5,53)(6,52)(7,51)(8,50)(9,49)(10,48)(11,47)(12,46)(13,45)(14,44)(15,43)(16,42)(17,41)(18,40)(19,39)(20,38)(21,37)(22,36)(23,35)(24,34)(25,33)(26,32)(27,31)(28,30), (2,8,50)(3,15,42)(4,22,34)(5,29,26)(6,36,18)(7,43,10)(9,57,51)(11,14,35)(12,21,27)(13,28,19)(16,49,52)(17,56,44)(23,41,53)(24,48,45)(25,55,37)(30,33,54)(31,40,46)(32,47,38) );

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)], [(1,57),(2,56),(3,55),(4,54),(5,53),(6,52),(7,51),(8,50),(9,49),(10,48),(11,47),(12,46),(13,45),(14,44),(15,43),(16,42),(17,41),(18,40),(19,39),(20,38),(21,37),(22,36),(23,35),(24,34),(25,33),(26,32),(27,31),(28,30)], [(2,8,50),(3,15,42),(4,22,34),(5,29,26),(6,36,18),(7,43,10),(9,57,51),(11,14,35),(12,21,27),(13,28,19),(16,49,52),(17,56,44),(23,41,53),(24,48,45),(25,55,37),(30,33,54),(31,40,46),(32,47,38)]])

Matrix representation of D₅₇⋊C₃ ►in GL₆(𝔽₂₂₉)

152	46	184	198	66	181
99	209	42	112	24	160
132	32	180	224	62	37
62	222	151	214	17	124
225	175	52	16	213	22
182	161	178	202	192	119

196	31	45	150	195	140
106	83	188	8	147	70
17	96	176	101	68	225
83	115	9	198	12	144
25	119	164	219	82	37
62	168	62	27	172	181

1	127	223	125	103	108
0	0	1	0	0	0
103	125	223	127	1	1
0	0	0	0	0	1
29	196	51	75	131	102
28	69	177	178	29	103

G:=sub<GL(6,GF(229))| [152,99,132,62,225,182,46,209,32,222,175,161,184,42,180,151,52,178,198,112,224,214,16,202,66,24,62,17,213,192,181,160,37,124,22,119],[196,106,17,83,25,62,31,83,96,115,119,168,45,188,176,9,164,62,150,8,101,198,219,27,195,147,68,12,82,172,140,70,225,144,37,181],[1,0,103,0,29,28,127,0,125,0,196,69,223,1,223,0,51,177,125,0,127,0,75,178,103,0,1,0,131,29,108,0,1,1,102,103] >;

D₅₇⋊C₃ in GAP, Magma, Sage, TeX

D_{57}\rtimes C_3

% in TeX

G:=Group("D57:C3");

// GroupNames label

G:=SmallGroup(342,11);

// by ID

G=gap.SmallGroup(342,11);

# by ID

G:=PCGroup([4,-2,-3,-3,-19,146,5187,1015]);

// Polycyclic

G:=Group<a,b,c|a^57=b^2=c^3=1,b*a*b=a^-1,c*a*c^-1=a^49,c*b*c^-1=a^48*b>;

// generators/relations

Export

Subgroup lattice of D₅₇⋊C₃ in TeX
Character table of D₅₇⋊C₃ in TeX

152	46	184	198	66	181
99	209	42	112	24	160
132	32	180	224	62	37
62	222	151	214	17	124
225	175	52	16	213	22
182	161	178	202	192	119

196	31	45	150	195	140
106	83	188	8	147	70
17	96	176	101	68	225
83	115	9	198	12	144
25	119	164	219	82	37
62	168	62	27	172	181

1	127	223	125	103	108
0	0	1	0	0	0
103	125	223	127	1	1
0	0	0	0	0	1
29	196	51	75	131	102
28	69	177	178	29	103

152	46	184	198	66	181
99	209	42	112	24	160
132	32	180	224	62	37
62	222	151	214	17	124
225	175	52	16	213	22
182	161	178	202	192	119

196	31	45	150	195	140
106	83	188	8	147	70
17	96	176	101	68	225
83	115	9	198	12	144
25	119	164	219	82	37
62	168	62	27	172	181

1	127	223	125	103	108
0	0	1	0	0	0
103	125	223	127	1	1
0	0	0	0	0	1
29	196	51	75	131	102
28	69	177	178	29	103

G = D57⋊C3 order 342 = 2·32·19

The semidirect product of D57 and C3 acting faithfully

G = D₅₇⋊C₃ order 342 = 2·3²·19

The semidirect product of D₅₇ and C₃ acting faithfully

152	46	184	198	66	181
99	209	42	112	24	160
132	32	180	224	62	37
62	222	151	214	17	124
225	175	52	16	213	22
182	161	178	202	192	119

196	31	45	150	195	140
106	83	188	8	147	70
17	96	176	101	68	225
83	115	9	198	12	144
25	119	164	219	82	37
62	168	62	27	172	181

1	127	223	125	103	108
0	0	1	0	0	0
103	125	223	127	1	1
0	0	0	0	0	1
29	196	51	75	131	102
28	69	177	178	29	103