direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C3×Q8⋊3Q8, C6.1222- 1+4, Q8⋊4(C3×Q8), (C3×Q8)⋊10Q8, C4⋊Q8.13C6, C4.19(C6×Q8), (C4×Q8).15C6, C42.51(C2×C6), (Q8×C12).22C2, C12.125(C2×Q8), C42.C2.6C6, C6.65(C22×Q8), (C2×C6).377C24, C12.348(C4○D4), (C4×C12).292C22, (C2×C12).715C23, C22.51(C23×C6), (C6×Q8).278C22, C2.14(C3×2- 1+4), C2.11(Q8×C2×C6), C4⋊C4.77(C2×C6), C4.46(C3×C4○D4), C2.30(C6×C4○D4), (C3×C4⋊Q8).28C2, C6.249(C2×C4○D4), (C2×Q8).78(C2×C6), (C2×C4).63(C22×C6), (C3×C4⋊C4).402C22, (C3×C42.C2).13C2, SmallGroup(192,1446)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C3×Q8⋊3Q8
G = < a,b,c,d,e | a3=b4=d4=1, c2=b2, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, cd=dc, ece-1=b2c, ede-1=d-1 >
Subgroups: 234 in 200 conjugacy classes, 166 normal (20 characteristic)
C1, C2, C3, C4, C4, C22, C6, C2×C4, C2×C4, Q8, Q8, C12, C12, C2×C6, C42, C4⋊C4, C4⋊C4, C2×Q8, C2×Q8, C2×C12, C2×C12, C3×Q8, C3×Q8, C4×Q8, C4×Q8, C42.C2, C4⋊Q8, C4×C12, C3×C4⋊C4, C3×C4⋊C4, C6×Q8, C6×Q8, Q8⋊3Q8, Q8×C12, Q8×C12, C3×C42.C2, C3×C4⋊Q8, C3×Q8⋊3Q8
Quotients: C1, C2, C3, C22, C6, Q8, C23, C2×C6, C2×Q8, C4○D4, C24, C3×Q8, C22×C6, C22×Q8, C2×C4○D4, 2- 1+4, C6×Q8, C3×C4○D4, C23×C6, Q8⋊3Q8, Q8×C2×C6, C6×C4○D4, C3×2- 1+4, C3×Q8⋊3Q8
►Regular action on 192 points
Generators in S192
(1 26 23)(2 27 24)(3 28 21)(4 25 22)(5 9 18)(6 10 19)(7 11 20)(8 12 17)(13 189 178)(14 190 179)(15 191 180)(16 192 177)(29 38 42)(30 39 43)(31 40 44)(32 37 41)(33 51 46)(34 52 47)(35 49 48)(36 50 45)(53 64 68)(54 61 65)(55 62 66)(56 63 67)(57 73 72)(58 74 69)(59 75 70)(60 76 71)(77 88 92)(78 85 89)(79 86 90)(80 87 91)(81 99 96)(82 100 93)(83 97 94)(84 98 95)(101 110 114)(102 111 115)(103 112 116)(104 109 113)(105 121 118)(106 122 119)(107 123 120)(108 124 117)(125 134 138)(126 135 139)(127 136 140)(128 133 137)(129 147 142)(130 148 143)(131 145 144)(132 146 141)(149 160 164)(150 157 161)(151 158 162)(152 159 163)(153 169 168)(154 170 165)(155 171 166)(156 172 167)(173 184 188)(174 181 185)(175 182 186)(176 183 187)
(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 64 3 62)(2 63 4 61)(5 57 7 59)(6 60 8 58)(9 73 11 75)(10 76 12 74)(13 140 15 138)(14 139 16 137)(17 69 19 71)(18 72 20 70)(21 55 23 53)(22 54 24 56)(25 65 27 67)(26 68 28 66)(29 95 31 93)(30 94 32 96)(33 85 35 87)(34 88 36 86)(37 81 39 83)(38 84 40 82)(41 99 43 97)(42 98 44 100)(45 79 47 77)(46 78 48 80)(49 91 51 89)(50 90 52 92)(101 165 103 167)(102 168 104 166)(105 159 107 157)(106 158 108 160)(109 155 111 153)(110 154 112 156)(113 171 115 169)(114 170 116 172)(117 149 119 151)(118 152 120 150)(121 163 123 161)(122 162 124 164)(125 189 127 191)(126 192 128 190)(129 183 131 181)(130 182 132 184)(133 179 135 177)(134 178 136 180)(141 173 143 175)(142 176 144 174)(145 185 147 187)(146 188 148 186)
(1 38 6 34)(2 39 7 35)(3 40 8 36)(4 37 5 33)(9 51 25 41)(10 52 26 42)(11 49 27 43)(12 50 28 44)(13 162 186 170)(14 163 187 171)(15 164 188 172)(16 161 185 169)(17 45 21 31)(18 46 22 32)(19 47 23 29)(20 48 24 30)(53 95 71 77)(54 96 72 78)(55 93 69 79)(56 94 70 80)(57 85 61 81)(58 86 62 82)(59 87 63 83)(60 88 64 84)(65 99 73 89)(66 100 74 90)(67 97 75 91)(68 98 76 92)(101 125 119 143)(102 126 120 144)(103 127 117 141)(104 128 118 142)(105 129 109 133)(106 130 110 134)(107 131 111 135)(108 132 112 136)(113 137 121 147)(114 138 122 148)(115 139 123 145)(116 140 124 146)(149 173 167 191)(150 174 168 192)(151 175 165 189)(152 176 166 190)(153 177 157 181)(154 178 158 182)(155 179 159 183)(156 180 160 184)
(1 110 6 106)(2 111 7 107)(3 112 8 108)(4 109 5 105)(9 121 25 113)(10 122 26 114)(11 123 27 115)(12 124 28 116)(13 100 186 90)(14 97 187 91)(15 98 188 92)(16 99 185 89)(17 117 21 103)(18 118 22 104)(19 119 23 101)(20 120 24 102)(29 143 47 125)(30 144 48 126)(31 141 45 127)(32 142 46 128)(33 133 37 129)(34 134 38 130)(35 135 39 131)(36 136 40 132)(41 147 51 137)(42 148 52 138)(43 145 49 139)(44 146 50 140)(53 167 71 149)(54 168 72 150)(55 165 69 151)(56 166 70 152)(57 157 61 153)(58 158 62 154)(59 159 63 155)(60 160 64 156)(65 169 73 161)(66 170 74 162)(67 171 75 163)(68 172 76 164)(77 191 95 173)(78 192 96 174)(79 189 93 175)(80 190 94 176)(81 181 85 177)(82 182 86 178)(83 183 87 179)(84 184 88 180)
G:=sub<Sym(192)| (1,26,23)(2,27,24)(3,28,21)(4,25,22)(5,9,18)(6,10,19)(7,11,20)(8,12,17)(13,189,178)(14,190,179)(15,191,180)(16,192,177)(29,38,42)(30,39,43)(31,40,44)(32,37,41)(33,51,46)(34,52,47)(35,49,48)(36,50,45)(53,64,68)(54,61,65)(55,62,66)(56,63,67)(57,73,72)(58,74,69)(59,75,70)(60,76,71)(77,88,92)(78,85,89)(79,86,90)(80,87,91)(81,99,96)(82,100,93)(83,97,94)(84,98,95)(101,110,114)(102,111,115)(103,112,116)(104,109,113)(105,121,118)(106,122,119)(107,123,120)(108,124,117)(125,134,138)(126,135,139)(127,136,140)(128,133,137)(129,147,142)(130,148,143)(131,145,144)(132,146,141)(149,160,164)(150,157,161)(151,158,162)(152,159,163)(153,169,168)(154,170,165)(155,171,166)(156,172,167)(173,184,188)(174,181,185)(175,182,186)(176,183,187), (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), (1,64,3,62)(2,63,4,61)(5,57,7,59)(6,60,8,58)(9,73,11,75)(10,76,12,74)(13,140,15,138)(14,139,16,137)(17,69,19,71)(18,72,20,70)(21,55,23,53)(22,54,24,56)(25,65,27,67)(26,68,28,66)(29,95,31,93)(30,94,32,96)(33,85,35,87)(34,88,36,86)(37,81,39,83)(38,84,40,82)(41,99,43,97)(42,98,44,100)(45,79,47,77)(46,78,48,80)(49,91,51,89)(50,90,52,92)(101,165,103,167)(102,168,104,166)(105,159,107,157)(106,158,108,160)(109,155,111,153)(110,154,112,156)(113,171,115,169)(114,170,116,172)(117,149,119,151)(118,152,120,150)(121,163,123,161)(122,162,124,164)(125,189,127,191)(126,192,128,190)(129,183,131,181)(130,182,132,184)(133,179,135,177)(134,178,136,180)(141,173,143,175)(142,176,144,174)(145,185,147,187)(146,188,148,186), (1,38,6,34)(2,39,7,35)(3,40,8,36)(4,37,5,33)(9,51,25,41)(10,52,26,42)(11,49,27,43)(12,50,28,44)(13,162,186,170)(14,163,187,171)(15,164,188,172)(16,161,185,169)(17,45,21,31)(18,46,22,32)(19,47,23,29)(20,48,24,30)(53,95,71,77)(54,96,72,78)(55,93,69,79)(56,94,70,80)(57,85,61,81)(58,86,62,82)(59,87,63,83)(60,88,64,84)(65,99,73,89)(66,100,74,90)(67,97,75,91)(68,98,76,92)(101,125,119,143)(102,126,120,144)(103,127,117,141)(104,128,118,142)(105,129,109,133)(106,130,110,134)(107,131,111,135)(108,132,112,136)(113,137,121,147)(114,138,122,148)(115,139,123,145)(116,140,124,146)(149,173,167,191)(150,174,168,192)(151,175,165,189)(152,176,166,190)(153,177,157,181)(154,178,158,182)(155,179,159,183)(156,180,160,184), (1,110,6,106)(2,111,7,107)(3,112,8,108)(4,109,5,105)(9,121,25,113)(10,122,26,114)(11,123,27,115)(12,124,28,116)(13,100,186,90)(14,97,187,91)(15,98,188,92)(16,99,185,89)(17,117,21,103)(18,118,22,104)(19,119,23,101)(20,120,24,102)(29,143,47,125)(30,144,48,126)(31,141,45,127)(32,142,46,128)(33,133,37,129)(34,134,38,130)(35,135,39,131)(36,136,40,132)(41,147,51,137)(42,148,52,138)(43,145,49,139)(44,146,50,140)(53,167,71,149)(54,168,72,150)(55,165,69,151)(56,166,70,152)(57,157,61,153)(58,158,62,154)(59,159,63,155)(60,160,64,156)(65,169,73,161)(66,170,74,162)(67,171,75,163)(68,172,76,164)(77,191,95,173)(78,192,96,174)(79,189,93,175)(80,190,94,176)(81,181,85,177)(82,182,86,178)(83,183,87,179)(84,184,88,180)>;
G:=Group( (1,26,23)(2,27,24)(3,28,21)(4,25,22)(5,9,18)(6,10,19)(7,11,20)(8,12,17)(13,189,178)(14,190,179)(15,191,180)(16,192,177)(29,38,42)(30,39,43)(31,40,44)(32,37,41)(33,51,46)(34,52,47)(35,49,48)(36,50,45)(53,64,68)(54,61,65)(55,62,66)(56,63,67)(57,73,72)(58,74,69)(59,75,70)(60,76,71)(77,88,92)(78,85,89)(79,86,90)(80,87,91)(81,99,96)(82,100,93)(83,97,94)(84,98,95)(101,110,114)(102,111,115)(103,112,116)(104,109,113)(105,121,118)(106,122,119)(107,123,120)(108,124,117)(125,134,138)(126,135,139)(127,136,140)(128,133,137)(129,147,142)(130,148,143)(131,145,144)(132,146,141)(149,160,164)(150,157,161)(151,158,162)(152,159,163)(153,169,168)(154,170,165)(155,171,166)(156,172,167)(173,184,188)(174,181,185)(175,182,186)(176,183,187), (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), (1,64,3,62)(2,63,4,61)(5,57,7,59)(6,60,8,58)(9,73,11,75)(10,76,12,74)(13,140,15,138)(14,139,16,137)(17,69,19,71)(18,72,20,70)(21,55,23,53)(22,54,24,56)(25,65,27,67)(26,68,28,66)(29,95,31,93)(30,94,32,96)(33,85,35,87)(34,88,36,86)(37,81,39,83)(38,84,40,82)(41,99,43,97)(42,98,44,100)(45,79,47,77)(46,78,48,80)(49,91,51,89)(50,90,52,92)(101,165,103,167)(102,168,104,166)(105,159,107,157)(106,158,108,160)(109,155,111,153)(110,154,112,156)(113,171,115,169)(114,170,116,172)(117,149,119,151)(118,152,120,150)(121,163,123,161)(122,162,124,164)(125,189,127,191)(126,192,128,190)(129,183,131,181)(130,182,132,184)(133,179,135,177)(134,178,136,180)(141,173,143,175)(142,176,144,174)(145,185,147,187)(146,188,148,186), (1,38,6,34)(2,39,7,35)(3,40,8,36)(4,37,5,33)(9,51,25,41)(10,52,26,42)(11,49,27,43)(12,50,28,44)(13,162,186,170)(14,163,187,171)(15,164,188,172)(16,161,185,169)(17,45,21,31)(18,46,22,32)(19,47,23,29)(20,48,24,30)(53,95,71,77)(54,96,72,78)(55,93,69,79)(56,94,70,80)(57,85,61,81)(58,86,62,82)(59,87,63,83)(60,88,64,84)(65,99,73,89)(66,100,74,90)(67,97,75,91)(68,98,76,92)(101,125,119,143)(102,126,120,144)(103,127,117,141)(104,128,118,142)(105,129,109,133)(106,130,110,134)(107,131,111,135)(108,132,112,136)(113,137,121,147)(114,138,122,148)(115,139,123,145)(116,140,124,146)(149,173,167,191)(150,174,168,192)(151,175,165,189)(152,176,166,190)(153,177,157,181)(154,178,158,182)(155,179,159,183)(156,180,160,184), (1,110,6,106)(2,111,7,107)(3,112,8,108)(4,109,5,105)(9,121,25,113)(10,122,26,114)(11,123,27,115)(12,124,28,116)(13,100,186,90)(14,97,187,91)(15,98,188,92)(16,99,185,89)(17,117,21,103)(18,118,22,104)(19,119,23,101)(20,120,24,102)(29,143,47,125)(30,144,48,126)(31,141,45,127)(32,142,46,128)(33,133,37,129)(34,134,38,130)(35,135,39,131)(36,136,40,132)(41,147,51,137)(42,148,52,138)(43,145,49,139)(44,146,50,140)(53,167,71,149)(54,168,72,150)(55,165,69,151)(56,166,70,152)(57,157,61,153)(58,158,62,154)(59,159,63,155)(60,160,64,156)(65,169,73,161)(66,170,74,162)(67,171,75,163)(68,172,76,164)(77,191,95,173)(78,192,96,174)(79,189,93,175)(80,190,94,176)(81,181,85,177)(82,182,86,178)(83,183,87,179)(84,184,88,180) );
G=PermutationGroup([[(1,26,23),(2,27,24),(3,28,21),(4,25,22),(5,9,18),(6,10,19),(7,11,20),(8,12,17),(13,189,178),(14,190,179),(15,191,180),(16,192,177),(29,38,42),(30,39,43),(31,40,44),(32,37,41),(33,51,46),(34,52,47),(35,49,48),(36,50,45),(53,64,68),(54,61,65),(55,62,66),(56,63,67),(57,73,72),(58,74,69),(59,75,70),(60,76,71),(77,88,92),(78,85,89),(79,86,90),(80,87,91),(81,99,96),(82,100,93),(83,97,94),(84,98,95),(101,110,114),(102,111,115),(103,112,116),(104,109,113),(105,121,118),(106,122,119),(107,123,120),(108,124,117),(125,134,138),(126,135,139),(127,136,140),(128,133,137),(129,147,142),(130,148,143),(131,145,144),(132,146,141),(149,160,164),(150,157,161),(151,158,162),(152,159,163),(153,169,168),(154,170,165),(155,171,166),(156,172,167),(173,184,188),(174,181,185),(175,182,186),(176,183,187)], [(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)], [(1,64,3,62),(2,63,4,61),(5,57,7,59),(6,60,8,58),(9,73,11,75),(10,76,12,74),(13,140,15,138),(14,139,16,137),(17,69,19,71),(18,72,20,70),(21,55,23,53),(22,54,24,56),(25,65,27,67),(26,68,28,66),(29,95,31,93),(30,94,32,96),(33,85,35,87),(34,88,36,86),(37,81,39,83),(38,84,40,82),(41,99,43,97),(42,98,44,100),(45,79,47,77),(46,78,48,80),(49,91,51,89),(50,90,52,92),(101,165,103,167),(102,168,104,166),(105,159,107,157),(106,158,108,160),(109,155,111,153),(110,154,112,156),(113,171,115,169),(114,170,116,172),(117,149,119,151),(118,152,120,150),(121,163,123,161),(122,162,124,164),(125,189,127,191),(126,192,128,190),(129,183,131,181),(130,182,132,184),(133,179,135,177),(134,178,136,180),(141,173,143,175),(142,176,144,174),(145,185,147,187),(146,188,148,186)], [(1,38,6,34),(2,39,7,35),(3,40,8,36),(4,37,5,33),(9,51,25,41),(10,52,26,42),(11,49,27,43),(12,50,28,44),(13,162,186,170),(14,163,187,171),(15,164,188,172),(16,161,185,169),(17,45,21,31),(18,46,22,32),(19,47,23,29),(20,48,24,30),(53,95,71,77),(54,96,72,78),(55,93,69,79),(56,94,70,80),(57,85,61,81),(58,86,62,82),(59,87,63,83),(60,88,64,84),(65,99,73,89),(66,100,74,90),(67,97,75,91),(68,98,76,92),(101,125,119,143),(102,126,120,144),(103,127,117,141),(104,128,118,142),(105,129,109,133),(106,130,110,134),(107,131,111,135),(108,132,112,136),(113,137,121,147),(114,138,122,148),(115,139,123,145),(116,140,124,146),(149,173,167,191),(150,174,168,192),(151,175,165,189),(152,176,166,190),(153,177,157,181),(154,178,158,182),(155,179,159,183),(156,180,160,184)], [(1,110,6,106),(2,111,7,107),(3,112,8,108),(4,109,5,105),(9,121,25,113),(10,122,26,114),(11,123,27,115),(12,124,28,116),(13,100,186,90),(14,97,187,91),(15,98,188,92),(16,99,185,89),(17,117,21,103),(18,118,22,104),(19,119,23,101),(20,120,24,102),(29,143,47,125),(30,144,48,126),(31,141,45,127),(32,142,46,128),(33,133,37,129),(34,134,38,130),(35,135,39,131),(36,136,40,132),(41,147,51,137),(42,148,52,138),(43,145,49,139),(44,146,50,140),(53,167,71,149),(54,168,72,150),(55,165,69,151),(56,166,70,152),(57,157,61,153),(58,158,62,154),(59,159,63,155),(60,160,64,156),(65,169,73,161),(66,170,74,162),(67,171,75,163),(68,172,76,164),(77,191,95,173),(78,192,96,174),(79,189,93,175),(80,190,94,176),(81,181,85,177),(82,182,86,178),(83,183,87,179),(84,184,88,180)]])
75 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 4A | ··· | 4L | 4M | ··· | 4U | 6A | ··· | 6F | 12A | ··· | 12X | 12Y | ··· | 12AP |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 4 | ··· | 4 | 4 | ··· | 4 | 6 | ··· | 6 | 12 | ··· | 12 | 12 | ··· | 12 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 |
75 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | - | - | ||||||||
| image | C1 | C2 | C2 | C2 | C3 | C6 | C6 | C6 | Q8 | C4○D4 | C3×Q8 | C3×C4○D4 | 2- 1+4 | C3×2- 1+4 |
| kernel | C3×Q8⋊3Q8 | Q8×C12 | C3×C42.C2 | C3×C4⋊Q8 | Q8⋊3Q8 | C4×Q8 | C42.C2 | C4⋊Q8 | C3×Q8 | C12 | Q8 | C4 | C6 | C2 |
| # reps | 1 | 6 | 6 | 3 | 2 | 12 | 12 | 6 | 4 | 4 | 8 | 8 | 1 | 2 |
Matrix representation of C3×Q8⋊3Q8 ►in GL4(𝔽13) generated by
| 3 | 0 | 0 | 0 |
| 0 | 3 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 |
| 12 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 8 | 0 | 0 |
| 8 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 12 | 0 |
| 0 | 5 | 0 | 0 |
| 8 | 0 | 0 | 0 |
| 0 | 0 | 4 | 3 |
| 0 | 0 | 3 | 9 |
G:=sub<GL(4,GF(13))| [3,0,0,0,0,3,0,0,0,0,1,0,0,0,0,1],[0,12,0,0,1,0,0,0,0,0,1,0,0,0,0,1],[0,8,0,0,8,0,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,0,12,0,0,1,0],[0,8,0,0,5,0,0,0,0,0,4,3,0,0,3,9] >;
C3×Q8⋊3Q8 in GAP, Magma, Sage, TeX
C_3\times Q_8\rtimes_3Q_8
% in TeX
G:=Group("C3xQ8:3Q8"); // GroupNames label
G:=SmallGroup(192,1446);
// by ID
G=gap.SmallGroup(192,1446);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-2,-2,672,701,344,2102,520,794,192]);
// Polycyclic
G:=Group<a,b,c,d,e|a^3=b^4=d^4=1,c^2=b^2,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e^-1=b^2*c,e*d*e^-1=d^-1>;
// generators/relations