C3:Q64 - GroupNames

class	1	2	3	4A	4B	4C	6	8A	8B	12A	12B	12C	16A	16B	16C	16D	24A	24B	32A	32B	32C	32D	32E	32F	32G	32H	48A	48B	48C	48D
size	1	1	2	2	16	48	2	2	2	4	16	16	2	2	2	2	4	4	6	6	6	6	6	6	6	6	4	4	4	4
ρ₁	1	1	1	1	1	1	1	1	1	1	1	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	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	linear of order 2
ρ₃	1	1	1	1	-1	1	1	1	1	1	-1	-1	1	1	1	1	1	1	-1	-1	-1	-1	-1	-1	-1	-1	1	1	1	1	linear of order 2
ρ₄	1	1	1	1	-1	-1	1	1	1	1	-1	-1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	linear of order 2
ρ₅	2	2	-1	2	2	0	-1	2	2	-1	-1	-1	2	2	2	2	-1	-1	0	0	0	0	0	0	0	0	-1	-1	-1	-1	orthogonal lifted from S₃
ρ₆	2	2	-1	2	-2	0	-1	2	2	-1	1	1	2	2	2	2	-1	-1	0	0	0	0	0	0	0	0	-1	-1	-1	-1	orthogonal lifted from D₆
ρ₇	2	2	2	2	0	0	2	2	2	2	0	0	-2	-2	-2	-2	2	2	0	0	0	0	0	0	0	0	-2	-2	-2	-2	orthogonal lifted from D₄
ρ₈	2	2	2	-2	0	0	2	0	0	-2	0	0	√2	-√2	-√2	√2	0	0	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-√2	√2	-√2	√2	orthogonal lifted from D₁₆
ρ₉	2	2	2	-2	0	0	2	0	0	-2	0	0	-√2	√2	√2	-√2	0	0	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁷-ζ₁₆	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁷+ζ₁₆	√2	-√2	√2	-√2	orthogonal lifted from D₁₆
ρ₁₀	2	2	2	2	0	0	2	-2	-2	2	0	0	0	0	0	0	-2	-2	-√2	√2	√2	√2	-√2	-√2	-√2	√2	0	0	0	0	orthogonal lifted from D₈
ρ₁₁	2	2	2	2	0	0	2	-2	-2	2	0	0	0	0	0	0	-2	-2	√2	-√2	-√2	-√2	√2	√2	√2	-√2	0	0	0	0	orthogonal lifted from D₈
ρ₁₂	2	2	2	-2	0	0	2	0	0	-2	0	0	-√2	√2	√2	-√2	0	0	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	ζ₁₆⁷-ζ₁₆	√2	-√2	√2	-√2	orthogonal lifted from D₁₆
ρ₁₃	2	2	2	-2	0	0	2	0	0	-2	0	0	√2	-√2	-√2	√2	0	0	ζ₁₆⁷-ζ₁₆	ζ₁₆⁵-ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁷-ζ₁₆	ζ₁₆⁵-ζ₁₆³	-√2	√2	-√2	√2	orthogonal lifted from D₁₆
ρ₁₄	2	-2	2	0	0	0	-2	√2	-√2	0	0	0	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	√2	-√2	ζ₃₂⁹-ζ₃₂⁷	-ζ₃₂²⁷+ζ₃₂²¹	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹³+ζ₃₂³	-ζ₃₂³¹+ζ₃₂¹⁷	ζ₃₂³¹-ζ₃₂¹⁷	-ζ₃₂⁹+ζ₃₂⁷	ζ₃₂²⁷-ζ₃₂²¹	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	symplectic lifted from Q₆₄, Schur index 2
ρ₁₅	2	-2	2	0	0	0	-2	√2	-√2	0	0	0	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	√2	-√2	-ζ₃₂³¹+ζ₃₂¹⁷	-ζ₃₂¹³+ζ₃₂³	-ζ₃₂²⁷+ζ₃₂²¹	ζ₃₂²⁷-ζ₃₂²¹	-ζ₃₂⁹+ζ₃₂⁷	ζ₃₂⁹-ζ₃₂⁷	ζ₃₂³¹-ζ₃₂¹⁷	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	symplectic lifted from Q₆₄, Schur index 2
ρ₁₆	2	-2	2	0	0	0	-2	√2	-√2	0	0	0	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	√2	-√2	ζ₃₂³¹-ζ₃₂¹⁷	ζ₃₂¹³-ζ₃₂³	ζ₃₂²⁷-ζ₃₂²¹	-ζ₃₂²⁷+ζ₃₂²¹	ζ₃₂⁹-ζ₃₂⁷	-ζ₃₂⁹+ζ₃₂⁷	-ζ₃₂³¹+ζ₃₂¹⁷	-ζ₃₂¹³+ζ₃₂³	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	symplectic lifted from Q₆₄, Schur index 2
ρ₁₇	2	-2	2	0	0	0	-2	√2	-√2	0	0	0	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	-ζ₃₂¹⁰+ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	√2	-√2	-ζ₃₂⁹+ζ₃₂⁷	ζ₃₂²⁷-ζ₃₂²¹	-ζ₃₂¹³+ζ₃₂³	ζ₃₂¹³-ζ₃₂³	ζ₃₂³¹-ζ₃₂¹⁷	-ζ₃₂³¹+ζ₃₂¹⁷	ζ₃₂⁹-ζ₃₂⁷	-ζ₃₂²⁷+ζ₃₂²¹	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	symplectic lifted from Q₆₄, Schur index 2
ρ₁₈	2	-2	2	0	0	0	-2	-√2	√2	0	0	0	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁴+ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	-√2	√2	ζ₃₂¹³-ζ₃₂³	ζ₃₂⁹-ζ₃₂⁷	ζ₃₂³¹-ζ₃₂¹⁷	-ζ₃₂³¹+ζ₃₂¹⁷	-ζ₃₂²⁷+ζ₃₂²¹	ζ₃₂²⁷-ζ₃₂²¹	-ζ₃₂¹³+ζ₃₂³	-ζ₃₂⁹+ζ₃₂⁷	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	symplectic lifted from Q₆₄, Schur index 2
ρ₁₉	2	-2	2	0	0	0	-2	-√2	√2	0	0	0	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁴-ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	-√2	√2	-ζ₃₂²⁷+ζ₃₂²¹	-ζ₃₂³¹+ζ₃₂¹⁷	ζ₃₂⁹-ζ₃₂⁷	-ζ₃₂⁹+ζ₃₂⁷	-ζ₃₂¹³+ζ₃₂³	ζ₃₂¹³-ζ₃₂³	ζ₃₂²⁷-ζ₃₂²¹	ζ₃₂³¹-ζ₃₂¹⁷	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	symplectic lifted from Q₆₄, Schur index 2
ρ₂₀	2	-2	2	0	0	0	-2	-√2	√2	0	0	0	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁴-ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	-√2	√2	ζ₃₂²⁷-ζ₃₂²¹	ζ₃₂³¹-ζ₃₂¹⁷	-ζ₃₂⁹+ζ₃₂⁷	ζ₃₂⁹-ζ₃₂⁷	ζ₃₂¹³-ζ₃₂³	-ζ₃₂¹³+ζ₃₂³	-ζ₃₂²⁷+ζ₃₂²¹	-ζ₃₂³¹+ζ₃₂¹⁷	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	symplectic lifted from Q₆₄, Schur index 2
ρ₂₁	2	-2	2	0	0	0	-2	-√2	√2	0	0	0	ζ₃₂¹⁰-ζ₃₂⁶	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁴+ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	-√2	√2	-ζ₃₂¹³+ζ₃₂³	-ζ₃₂⁹+ζ₃₂⁷	-ζ₃₂³¹+ζ₃₂¹⁷	ζ₃₂³¹-ζ₃₂¹⁷	ζ₃₂²⁷-ζ₃₂²¹	-ζ₃₂²⁷+ζ₃₂²¹	ζ₃₂¹³-ζ₃₂³	ζ₃₂⁹-ζ₃₂⁷	ζ₃₂¹⁴-ζ₃₂²	-ζ₃₂¹⁰+ζ₃₂⁶	-ζ₃₂¹⁴+ζ₃₂²	ζ₃₂¹⁰-ζ₃₂⁶	symplectic lifted from Q₆₄, Schur index 2
ρ₂₂	2	2	-1	2	0	0	-1	2	2	-1	-√-3	√-3	-2	-2	-2	-2	-1	-1	0	0	0	0	0	0	0	0	1	1	1	1	complex lifted from C₃⋊D₄
ρ₂₃	2	2	-1	2	0	0	-1	2	2	-1	√-3	-√-3	-2	-2	-2	-2	-1	-1	0	0	0	0	0	0	0	0	1	1	1	1	complex lifted from C₃⋊D₄
ρ₂₄	4	4	-2	4	0	0	-2	-4	-4	-2	0	0	0	0	0	0	2	2	0	0	0	0	0	0	0	0	0	0	0	0	orthogonal lifted from D₄⋊S₃, Schur index 2
ρ₂₅	4	4	-2	-4	0	0	-2	0	0	2	0	0	2√2	-2√2	-2√2	2√2	0	0	0	0	0	0	0	0	0	0	√2	-√2	√2	-√2	orthogonal lifted from C₃⋊D₁₆, Schur index 2
ρ₂₆	4	4	-2	-4	0	0	-2	0	0	2	0	0	-2√2	2√2	2√2	-2√2	0	0	0	0	0	0	0	0	0	0	-√2	√2	-√2	√2	orthogonal lifted from C₃⋊D₁₆, Schur index 2
ρ₂₇	4	-4	-2	0	0	0	2	-2√2	2√2	0	0	0	2ζ₁₆⁵-2ζ₁₆³	-2ζ₁₆¹⁵+2ζ₁₆⁹	2ζ₁₆¹⁵-2ζ₁₆⁹	-2ζ₁₆⁵+2ζ₁₆³	√2	-√2	0	0	0	0	0	0	0	0	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	symplectic faithful, Schur index 2
ρ₂₈	4	-4	-2	0	0	0	2	2√2	-2√2	0	0	0	-2ζ₁₆¹⁵+2ζ₁₆⁹	-2ζ₁₆⁵+2ζ₁₆³	2ζ₁₆⁵-2ζ₁₆³	2ζ₁₆¹⁵-2ζ₁₆⁹	-√2	√2	0	0	0	0	0	0	0	0	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	symplectic faithful, Schur index 2
ρ₂₉	4	-4	-2	0	0	0	2	-2√2	2√2	0	0	0	-2ζ₁₆⁵+2ζ₁₆³	2ζ₁₆¹⁵-2ζ₁₆⁹	-2ζ₁₆¹⁵+2ζ₁₆⁹	2ζ₁₆⁵-2ζ₁₆³	√2	-√2	0	0	0	0	0	0	0	0	ζ₁₆⁷-ζ₁₆	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	symplectic faithful, Schur index 2
ρ₃₀	4	-4	-2	0	0	0	2	2√2	-2√2	0	0	0	2ζ₁₆¹⁵-2ζ₁₆⁹	2ζ₁₆⁵-2ζ₁₆³	-2ζ₁₆⁵+2ζ₁₆³	-2ζ₁₆¹⁵+2ζ₁₆⁹	-√2	√2	0	0	0	0	0	0	0	0	-ζ₁₆⁵+ζ₁₆³	-ζ₁₆⁷+ζ₁₆	ζ₁₆⁵-ζ₁₆³	ζ₁₆⁷-ζ₁₆	symplectic faithful, Schur index 2

Smallest permutation representation of C₃⋊Q₆₄
►Regular action on 192 points

Generators in S₁₉₂

(1 184 39)(2 40 185)(3 186 41)(4 42 187)(5 188 43)(6 44 189)(7 190 45)(8 46 191)(9 192 47)(10 48 161)(11 162 49)(12 50 163)(13 164 51)(14 52 165)(15 166 53)(16 54 167)(17 168 55)(18 56 169)(19 170 57)(20 58 171)(21 172 59)(22 60 173)(23 174 61)(24 62 175)(25 176 63)(26 64 177)(27 178 33)(28 34 179)(29 180 35)(30 36 181)(31 182 37)(32 38 183)(65 155 98)(66 99 156)(67 157 100)(68 101 158)(69 159 102)(70 103 160)(71 129 104)(72 105 130)(73 131 106)(74 107 132)(75 133 108)(76 109 134)(77 135 110)(78 111 136)(79 137 112)(80 113 138)(81 139 114)(82 115 140)(83 141 116)(84 117 142)(85 143 118)(86 119 144)(87 145 120)(88 121 146)(89 147 122)(90 123 148)(91 149 124)(92 125 150)(93 151 126)(94 127 152)(95 153 128)(96 97 154)

(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 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128)(129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192)

(1 86 17 70)(2 85 18 69)(3 84 19 68)(4 83 20 67)(5 82 21 66)(6 81 22 65)(7 80 23 96)(8 79 24 95)(9 78 25 94)(10 77 26 93)(11 76 27 92)(12 75 28 91)(13 74 29 90)(14 73 30 89)(15 72 31 88)(16 71 32 87)(33 150 49 134)(34 149 50 133)(35 148 51 132)(36 147 52 131)(37 146 53 130)(38 145 54 129)(39 144 55 160)(40 143 56 159)(41 142 57 158)(42 141 58 157)(43 140 59 156)(44 139 60 155)(45 138 61 154)(46 137 62 153)(47 136 63 152)(48 135 64 151)(97 190 113 174)(98 189 114 173)(99 188 115 172)(100 187 116 171)(101 186 117 170)(102 185 118 169)(103 184 119 168)(104 183 120 167)(105 182 121 166)(106 181 122 165)(107 180 123 164)(108 179 124 163)(109 178 125 162)(110 177 126 161)(111 176 127 192)(112 175 128 191)

G:=sub<Sym(192)| (1,184,39)(2,40,185)(3,186,41)(4,42,187)(5,188,43)(6,44,189)(7,190,45)(8,46,191)(9,192,47)(10,48,161)(11,162,49)(12,50,163)(13,164,51)(14,52,165)(15,166,53)(16,54,167)(17,168,55)(18,56,169)(19,170,57)(20,58,171)(21,172,59)(22,60,173)(23,174,61)(24,62,175)(25,176,63)(26,64,177)(27,178,33)(28,34,179)(29,180,35)(30,36,181)(31,182,37)(32,38,183)(65,155,98)(66,99,156)(67,157,100)(68,101,158)(69,159,102)(70,103,160)(71,129,104)(72,105,130)(73,131,106)(74,107,132)(75,133,108)(76,109,134)(77,135,110)(78,111,136)(79,137,112)(80,113,138)(81,139,114)(82,115,140)(83,141,116)(84,117,142)(85,143,118)(86,119,144)(87,145,120)(88,121,146)(89,147,122)(90,123,148)(91,149,124)(92,125,150)(93,151,126)(94,127,152)(95,153,128)(96,97,154), (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)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192), (1,86,17,70)(2,85,18,69)(3,84,19,68)(4,83,20,67)(5,82,21,66)(6,81,22,65)(7,80,23,96)(8,79,24,95)(9,78,25,94)(10,77,26,93)(11,76,27,92)(12,75,28,91)(13,74,29,90)(14,73,30,89)(15,72,31,88)(16,71,32,87)(33,150,49,134)(34,149,50,133)(35,148,51,132)(36,147,52,131)(37,146,53,130)(38,145,54,129)(39,144,55,160)(40,143,56,159)(41,142,57,158)(42,141,58,157)(43,140,59,156)(44,139,60,155)(45,138,61,154)(46,137,62,153)(47,136,63,152)(48,135,64,151)(97,190,113,174)(98,189,114,173)(99,188,115,172)(100,187,116,171)(101,186,117,170)(102,185,118,169)(103,184,119,168)(104,183,120,167)(105,182,121,166)(106,181,122,165)(107,180,123,164)(108,179,124,163)(109,178,125,162)(110,177,126,161)(111,176,127,192)(112,175,128,191)>;

G:=Group( (1,184,39)(2,40,185)(3,186,41)(4,42,187)(5,188,43)(6,44,189)(7,190,45)(8,46,191)(9,192,47)(10,48,161)(11,162,49)(12,50,163)(13,164,51)(14,52,165)(15,166,53)(16,54,167)(17,168,55)(18,56,169)(19,170,57)(20,58,171)(21,172,59)(22,60,173)(23,174,61)(24,62,175)(25,176,63)(26,64,177)(27,178,33)(28,34,179)(29,180,35)(30,36,181)(31,182,37)(32,38,183)(65,155,98)(66,99,156)(67,157,100)(68,101,158)(69,159,102)(70,103,160)(71,129,104)(72,105,130)(73,131,106)(74,107,132)(75,133,108)(76,109,134)(77,135,110)(78,111,136)(79,137,112)(80,113,138)(81,139,114)(82,115,140)(83,141,116)(84,117,142)(85,143,118)(86,119,144)(87,145,120)(88,121,146)(89,147,122)(90,123,148)(91,149,124)(92,125,150)(93,151,126)(94,127,152)(95,153,128)(96,97,154), (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)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128)(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192), (1,86,17,70)(2,85,18,69)(3,84,19,68)(4,83,20,67)(5,82,21,66)(6,81,22,65)(7,80,23,96)(8,79,24,95)(9,78,25,94)(10,77,26,93)(11,76,27,92)(12,75,28,91)(13,74,29,90)(14,73,30,89)(15,72,31,88)(16,71,32,87)(33,150,49,134)(34,149,50,133)(35,148,51,132)(36,147,52,131)(37,146,53,130)(38,145,54,129)(39,144,55,160)(40,143,56,159)(41,142,57,158)(42,141,58,157)(43,140,59,156)(44,139,60,155)(45,138,61,154)(46,137,62,153)(47,136,63,152)(48,135,64,151)(97,190,113,174)(98,189,114,173)(99,188,115,172)(100,187,116,171)(101,186,117,170)(102,185,118,169)(103,184,119,168)(104,183,120,167)(105,182,121,166)(106,181,122,165)(107,180,123,164)(108,179,124,163)(109,178,125,162)(110,177,126,161)(111,176,127,192)(112,175,128,191) );

G=PermutationGroup([[(1,184,39),(2,40,185),(3,186,41),(4,42,187),(5,188,43),(6,44,189),(7,190,45),(8,46,191),(9,192,47),(10,48,161),(11,162,49),(12,50,163),(13,164,51),(14,52,165),(15,166,53),(16,54,167),(17,168,55),(18,56,169),(19,170,57),(20,58,171),(21,172,59),(22,60,173),(23,174,61),(24,62,175),(25,176,63),(26,64,177),(27,178,33),(28,34,179),(29,180,35),(30,36,181),(31,182,37),(32,38,183),(65,155,98),(66,99,156),(67,157,100),(68,101,158),(69,159,102),(70,103,160),(71,129,104),(72,105,130),(73,131,106),(74,107,132),(75,133,108),(76,109,134),(77,135,110),(78,111,136),(79,137,112),(80,113,138),(81,139,114),(82,115,140),(83,141,116),(84,117,142),(85,143,118),(86,119,144),(87,145,120),(88,121,146),(89,147,122),(90,123,148),(91,149,124),(92,125,150),(93,151,126),(94,127,152),(95,153,128),(96,97,154)], [(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),(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128),(129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192)], [(1,86,17,70),(2,85,18,69),(3,84,19,68),(4,83,20,67),(5,82,21,66),(6,81,22,65),(7,80,23,96),(8,79,24,95),(9,78,25,94),(10,77,26,93),(11,76,27,92),(12,75,28,91),(13,74,29,90),(14,73,30,89),(15,72,31,88),(16,71,32,87),(33,150,49,134),(34,149,50,133),(35,148,51,132),(36,147,52,131),(37,146,53,130),(38,145,54,129),(39,144,55,160),(40,143,56,159),(41,142,57,158),(42,141,58,157),(43,140,59,156),(44,139,60,155),(45,138,61,154),(46,137,62,153),(47,136,63,152),(48,135,64,151),(97,190,113,174),(98,189,114,173),(99,188,115,172),(100,187,116,171),(101,186,117,170),(102,185,118,169),(103,184,119,168),(104,183,120,167),(105,182,121,166),(106,181,122,165),(107,180,123,164),(108,179,124,163),(109,178,125,162),(110,177,126,161),(111,176,127,192),(112,175,128,191)]])

Matrix representation of C₃⋊Q₆₄ ►in GL₄(𝔽₉₇) generated by

1	0	0	0
0	1	0	0
0	0	0	1
0	0	96	96

27	57	0	0
40	27	0	0
0	0	47	80
0	0	33	50

13	86	0	0
86	84	0	0
0	0	56	15
0	0	82	41

G:=sub<GL(4,GF(97))| [1,0,0,0,0,1,0,0,0,0,0,96,0,0,1,96],[27,40,0,0,57,27,0,0,0,0,47,33,0,0,80,50],[13,86,0,0,86,84,0,0,0,0,56,82,0,0,15,41] >;

C₃⋊Q₆₄ in GAP, Magma, Sage, TeX

C_3\rtimes Q_{64}

% in TeX

G:=Group("C3:Q64");

// GroupNames label

G:=SmallGroup(192,81);

// by ID

G=gap.SmallGroup(192,81);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,224,85,232,254,135,142,675,346,192,1684,851,102,6278]);

// Polycyclic

G:=Group<a,b,c|a^3=b^32=1,c^2=b^16,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^-1>;

// generators/relations

Export

Subgroup lattice of C₃⋊Q₆₄ in TeX
Character table of C₃⋊Q₆₄ in TeX

G = C3⋊Q64 order 192 = 26·3

The semidirect product of C3 and Q64 acting via Q64/Q32=C2

G = C₃⋊Q₆₄ order 192 = 2⁶·3

The semidirect product of C₃ and Q₆₄ acting via Q₆₄/Q₃₂=C₂