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## G = (C2×Q8).36D6order 192 = 26·3

### 12nd non-split extension by C2×Q8 of D6 acting via D6/C3=C22

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C12 — (C2×Q8).36D6
 Chief series C1 — C3 — C6 — C12 — C2×C12 — C4×Dic3 — Dic3⋊Q8 — (C2×Q8).36D6
 Lower central C3 — C6 — C2×C12 — (C2×Q8).36D6
 Upper central C1 — C22 — C2×C4 — Q8⋊C4

Generators and relations for (C2×Q8).36D6
G = < a,b,c,d,e | a2=b4=1, c2=b2, d6=ab2, e2=a, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=dbd-1=ebe-1=b-1, dcd-1=ab-1c, ece-1=bc, ede-1=ad5 >

Subgroups: 232 in 90 conjugacy classes, 37 normal (all characteristic)
C1, C2, C3, C4, C4, C22, C6, C8, C2×C4, C2×C4, Q8, Dic3, C12, C12, C2×C6, C42, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C2×Q8, C2×Q8, C3⋊C8, C24, Dic6, C2×Dic3, C2×Dic3, C2×C12, C2×C12, C3×Q8, C8⋊C4, Q8⋊C4, Q8⋊C4, C42.C2, C4⋊Q8, C2×C3⋊C8, C4×Dic3, Dic3⋊C4, C4⋊Dic3, C4⋊Dic3, C3×C4⋊C4, C2×C24, C2×Dic6, C6×Q8, C42.30C22, C6.SD16, C24⋊C4, C2.Dic12, Q82Dic3, C3×Q8⋊C4, C4.Dic6, Dic3⋊Q8, (C2×Q8).36D6
Quotients: C1, C2, C22, S3, D4, C23, D6, C2×D4, C4○D4, C22×S3, C4.4D4, C8.C22, C4○D12, S3×D4, D42S3, C42.30C22, C23.11D6, D4.D6, Q16⋊S3, (C2×Q8).36D6

Character table of (C2×Q8).36D6

 class 1 2A 2B 2C 3 4A 4B 4C 4D 4E 4F 4G 4H 6A 6B 6C 8A 8B 8C 8D 12A 12B 12C 12D 12E 12F 24A 24B 24C 24D size 1 1 1 1 2 2 2 8 8 12 12 24 24 2 2 2 4 4 12 12 4 4 8 8 8 8 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 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 ρ6 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 ρ7 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 ρ8 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 ρ9 2 2 2 2 -1 2 2 2 2 0 0 0 0 -1 -1 -1 2 2 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 orthogonal lifted from S3 ρ10 2 2 2 2 -1 2 2 -2 -2 0 0 0 0 -1 -1 -1 2 2 0 0 -1 -1 1 1 1 1 -1 -1 -1 -1 orthogonal lifted from D6 ρ11 2 2 2 2 2 -2 -2 0 0 -2 2 0 0 2 2 2 0 0 0 0 -2 -2 0 0 0 0 0 0 0 0 orthogonal lifted from D4 ρ12 2 2 2 2 2 -2 -2 0 0 2 -2 0 0 2 2 2 0 0 0 0 -2 -2 0 0 0 0 0 0 0 0 orthogonal lifted from D4 ρ13 2 2 2 2 -1 2 2 2 -2 0 0 0 0 -1 -1 -1 -2 -2 0 0 -1 -1 1 -1 -1 1 1 1 1 1 orthogonal lifted from D6 ρ14 2 2 2 2 -1 2 2 -2 2 0 0 0 0 -1 -1 -1 -2 -2 0 0 -1 -1 -1 1 1 -1 1 1 1 1 orthogonal lifted from D6 ρ15 2 -2 2 -2 2 2 -2 0 0 0 0 0 0 2 -2 -2 2i -2i 0 0 2 -2 0 0 0 0 2i -2i -2i 2i complex lifted from C4○D4 ρ16 2 -2 2 -2 2 2 -2 0 0 0 0 0 0 2 -2 -2 -2i 2i 0 0 2 -2 0 0 0 0 -2i 2i 2i -2i complex lifted from C4○D4 ρ17 2 -2 2 -2 2 -2 2 0 0 0 0 0 0 2 -2 -2 0 0 -2i 2i -2 2 0 0 0 0 0 0 0 0 complex lifted from C4○D4 ρ18 2 -2 2 -2 2 -2 2 0 0 0 0 0 0 2 -2 -2 0 0 2i -2i -2 2 0 0 0 0 0 0 0 0 complex lifted from C4○D4 ρ19 2 -2 2 -2 -1 2 -2 0 0 0 0 0 0 -1 1 1 2i -2i 0 0 -1 1 -√3 -√-3 √-3 √3 -i i i -i complex lifted from C4○D12 ρ20 2 -2 2 -2 -1 2 -2 0 0 0 0 0 0 -1 1 1 2i -2i 0 0 -1 1 √3 √-3 -√-3 -√3 -i i i -i complex lifted from C4○D12 ρ21 2 -2 2 -2 -1 2 -2 0 0 0 0 0 0 -1 1 1 -2i 2i 0 0 -1 1 √3 -√-3 √-3 -√3 i -i -i i complex lifted from C4○D12 ρ22 2 -2 2 -2 -1 2 -2 0 0 0 0 0 0 -1 1 1 -2i 2i 0 0 -1 1 -√3 √-3 -√-3 √3 i -i -i i complex lifted from C4○D12 ρ23 4 4 4 4 -2 -4 -4 0 0 0 0 0 0 -2 -2 -2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 orthogonal lifted from S3×D4 ρ24 4 -4 4 -4 -2 -4 4 0 0 0 0 0 0 -2 2 2 0 0 0 0 2 -2 0 0 0 0 0 0 0 0 symplectic lifted from D4⋊2S3, Schur index 2 ρ25 4 -4 -4 4 4 0 0 0 0 0 0 0 0 -4 4 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 symplectic lifted from C8.C22, Schur index 2 ρ26 4 4 -4 -4 4 0 0 0 0 0 0 0 0 -4 -4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 symplectic lifted from C8.C22, Schur index 2 ρ27 4 4 -4 -4 -2 0 0 0 0 0 0 0 0 2 2 -2 0 0 0 0 0 0 0 0 0 0 √6 -√6 √6 -√6 symplectic lifted from D4.D6, Schur index 2 ρ28 4 4 -4 -4 -2 0 0 0 0 0 0 0 0 2 2 -2 0 0 0 0 0 0 0 0 0 0 -√6 √6 -√6 √6 symplectic lifted from D4.D6, Schur index 2 ρ29 4 -4 -4 4 -2 0 0 0 0 0 0 0 0 2 -2 2 0 0 0 0 0 0 0 0 0 0 √-6 √-6 -√-6 -√-6 complex lifted from Q16⋊S3 ρ30 4 -4 -4 4 -2 0 0 0 0 0 0 0 0 2 -2 2 0 0 0 0 0 0 0 0 0 0 -√-6 -√-6 √-6 √-6 complex lifted from Q16⋊S3

Smallest permutation representation of (C2×Q8).36D6
Regular action on 192 points
Generators in S192
(1 53)(2 54)(3 55)(4 56)(5 57)(6 58)(7 59)(8 60)(9 49)(10 50)(11 51)(12 52)(13 122)(14 123)(15 124)(16 125)(17 126)(18 127)(19 128)(20 129)(21 130)(22 131)(23 132)(24 121)(25 137)(26 138)(27 139)(28 140)(29 141)(30 142)(31 143)(32 144)(33 133)(34 134)(35 135)(36 136)(37 67)(38 68)(39 69)(40 70)(41 71)(42 72)(43 61)(44 62)(45 63)(46 64)(47 65)(48 66)(73 160)(74 161)(75 162)(76 163)(77 164)(78 165)(79 166)(80 167)(81 168)(82 157)(83 158)(84 159)(85 185)(86 186)(87 187)(88 188)(89 189)(90 190)(91 191)(92 192)(93 181)(94 182)(95 183)(96 184)(97 113)(98 114)(99 115)(100 116)(101 117)(102 118)(103 119)(104 120)(105 109)(106 110)(107 111)(108 112)(145 180)(146 169)(147 170)(148 171)(149 172)(150 173)(151 174)(152 175)(153 176)(154 177)(155 178)(156 179)
(1 192 59 86)(2 87 60 181)(3 182 49 88)(4 89 50 183)(5 184 51 90)(6 91 52 185)(7 186 53 92)(8 93 54 187)(9 188 55 94)(10 95 56 189)(11 190 57 96)(12 85 58 191)(13 69 128 45)(14 46 129 70)(15 71 130 47)(16 48 131 72)(17 61 132 37)(18 38 121 62)(19 63 122 39)(20 40 123 64)(21 65 124 41)(22 42 125 66)(23 67 126 43)(24 44 127 68)(25 100 143 110)(26 111 144 101)(27 102 133 112)(28 113 134 103)(29 104 135 114)(30 115 136 105)(31 106 137 116)(32 117 138 107)(33 108 139 118)(34 119 140 97)(35 98 141 120)(36 109 142 99)(73 173 166 156)(74 145 167 174)(75 175 168 146)(76 147 157 176)(77 177 158 148)(78 149 159 178)(79 179 160 150)(80 151 161 180)(81 169 162 152)(82 153 163 170)(83 171 164 154)(84 155 165 172)
(1 84 59 165)(2 179 60 150)(3 74 49 167)(4 169 50 152)(5 76 51 157)(6 171 52 154)(7 78 53 159)(8 173 54 156)(9 80 55 161)(10 175 56 146)(11 82 57 163)(12 177 58 148)(13 36 128 142)(14 106 129 116)(15 26 130 144)(16 108 131 118)(17 28 132 134)(18 98 121 120)(19 30 122 136)(20 100 123 110)(21 32 124 138)(22 102 125 112)(23 34 126 140)(24 104 127 114)(25 64 143 40)(27 66 133 42)(29 68 135 44)(31 70 137 46)(33 72 139 48)(35 62 141 38)(37 113 61 103)(39 115 63 105)(41 117 65 107)(43 119 67 97)(45 109 69 99)(47 111 71 101)(73 187 166 93)(75 189 168 95)(77 191 158 85)(79 181 160 87)(81 183 162 89)(83 185 164 91)(86 155 192 172)(88 145 182 174)(90 147 184 176)(92 149 186 178)(94 151 188 180)(96 153 190 170)
(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)
(1 115 53 99)(2 104 54 120)(3 113 55 97)(4 102 56 118)(5 111 57 107)(6 100 58 116)(7 109 59 105)(8 98 60 114)(9 119 49 103)(10 108 50 112)(11 117 51 101)(12 106 52 110)(13 165 122 78)(14 83 123 158)(15 163 124 76)(16 81 125 168)(17 161 126 74)(18 79 127 166)(19 159 128 84)(20 77 129 164)(21 157 130 82)(22 75 131 162)(23 167 132 80)(24 73 121 160)(25 191 137 91)(26 96 138 184)(27 189 139 89)(28 94 140 182)(29 187 141 87)(30 92 142 192)(31 185 143 85)(32 90 144 190)(33 183 133 95)(34 88 134 188)(35 181 135 93)(36 86 136 186)(37 180 67 145)(38 150 68 173)(39 178 69 155)(40 148 70 171)(41 176 71 153)(42 146 72 169)(43 174 61 151)(44 156 62 179)(45 172 63 149)(46 154 64 177)(47 170 65 147)(48 152 66 175)

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

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

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

Matrix representation of (C2×Q8).36D6 in GL8(𝔽73)

 72 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 72
,
 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 72 0 0 0 0 0 0 0 0 0 0 72 0 0 0 0 0 0 1 0
,
 40 12 11 41 0 0 0 0 61 28 21 11 0 0 0 0 4 37 45 61 0 0 0 0 40 4 12 33 0 0 0 0 0 0 0 0 70 61 71 2 0 0 0 0 61 3 71 71 0 0 0 0 2 2 12 70 0 0 0 0 71 2 70 61
,
 66 7 25 23 0 0 0 0 66 59 25 25 0 0 0 0 0 0 14 66 0 0 0 0 0 0 7 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
,
 30 43 62 69 0 0 0 0 13 43 69 15 0 0 0 0 0 0 20 55 0 0 0 0 0 0 2 53 0 0 0 0 0 0 0 0 24 8 35 0 0 0 0 0 8 49 0 35 0 0 0 0 38 0 49 65 0 0 0 0 0 38 65 24

G:=sub<GL(8,GF(73))| [72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,72],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,72,0],[40,61,4,40,0,0,0,0,12,28,37,4,0,0,0,0,11,21,45,12,0,0,0,0,41,11,61,33,0,0,0,0,0,0,0,0,70,61,2,71,0,0,0,0,61,3,2,2,0,0,0,0,71,71,12,70,0,0,0,0,2,71,70,61],[66,66,0,0,0,0,0,0,7,59,0,0,0,0,0,0,25,25,14,7,0,0,0,0,23,25,66,7,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[30,13,0,0,0,0,0,0,43,43,0,0,0,0,0,0,62,69,20,2,0,0,0,0,69,15,55,53,0,0,0,0,0,0,0,0,24,8,38,0,0,0,0,0,8,49,0,38,0,0,0,0,35,0,49,65,0,0,0,0,0,35,65,24] >;

(C2×Q8).36D6 in GAP, Magma, Sage, TeX

(C_2\times Q_8)._{36}D_6
% in TeX

G:=Group("(C2xQ8).36D6");
// GroupNames label

G:=SmallGroup(192,356);
// by ID

G=gap.SmallGroup(192,356);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-3,112,253,232,1094,135,100,570,297,136,6278]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^4=1,c^2=b^2,d^6=a*b^2,e^2=a,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=d*b*d^-1=e*b*e^-1=b^-1,d*c*d^-1=a*b^-1*c,e*c*e^-1=b*c,e*d*e^-1=a*d^5>;
// generators/relations

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