metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.93D14, (C4×D28)⋊9C2, C4⋊C4.270D14, (C4×Dic14)⋊9C2, (D7×C42)⋊18C2, D14⋊Q8⋊50C2, D14.1(C4○D4), D14⋊D4.6C2, C42⋊C2⋊12D7, C42⋊D7⋊30C2, Dic7.Q8⋊44C2, (C2×C14).72C24, C22⋊C4.96D14, D14.D4⋊52C2, D14.5D4⋊48C2, C28.255(C4○D4), C4.139(C4○D28), (C2×C28).147C23, (C4×C28).233C22, Dic7.2(C4○D4), (C22×C4).193D14, C23.84(C22×D7), D14⋊C4.143C22, Dic7.D4⋊48C2, (C2×D28).207C22, C23.D14⋊48C2, C4⋊Dic7.292C22, (C2×Dic7).25C23, C22.101(C23×D7), C23.D7.95C22, Dic7⋊C4.152C22, (C22×C28).377C22, (C22×C14).142C23, C7⋊2(C23.36C23), (C4×Dic7).196C22, (C22×D7).165C23, (C2×Dic14).230C22, (C4×C7⋊D4)⋊52C2, C2.11(D7×C4○D4), C4⋊C4⋊D7⋊49C2, C14.29(C2×C4○D4), C2.31(C2×C4○D28), (C2×C4×D7).290C22, (C7×C42⋊C2)⋊14C2, (C7×C4⋊C4).308C22, (C2×C4).150(C22×D7), (C2×C7⋊D4).102C22, (C7×C22⋊C4).112C22, SmallGroup(448,981)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.93D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, ac=ca, ad=da, cbc-1=a2b, dbd-1=b-1, dcd-1=c13 >
Subgroups: 1012 in 234 conjugacy classes, 99 normal (91 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C42, C42⋊C2, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C23.36C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C2×C7⋊D4, C22×C28, C4×Dic14, D7×C42, C42⋊D7, C4×D28, C23.D14, D14.D4, D14⋊D4, Dic7.D4, Dic7.Q8, D14.5D4, D14⋊Q8, C4⋊C4⋊D7, C4×C7⋊D4, C7×C42⋊C2, C42.93D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, C4○D28, C23×D7, C2×C4○D28, D7×C4○D4, C42.93D14
►On 224 points
Generators in S224
(1 171 132 48)(2 172 133 49)(3 173 134 50)(4 174 135 51)(5 175 136 52)(6 176 137 53)(7 177 138 54)(8 178 139 55)(9 179 140 56)(10 180 113 29)(11 181 114 30)(12 182 115 31)(13 183 116 32)(14 184 117 33)(15 185 118 34)(16 186 119 35)(17 187 120 36)(18 188 121 37)(19 189 122 38)(20 190 123 39)(21 191 124 40)(22 192 125 41)(23 193 126 42)(24 194 127 43)(25 195 128 44)(26 196 129 45)(27 169 130 46)(28 170 131 47)(57 94 199 159)(58 95 200 160)(59 96 201 161)(60 97 202 162)(61 98 203 163)(62 99 204 164)(63 100 205 165)(64 101 206 166)(65 102 207 167)(66 103 208 168)(67 104 209 141)(68 105 210 142)(69 106 211 143)(70 107 212 144)(71 108 213 145)(72 109 214 146)(73 110 215 147)(74 111 216 148)(75 112 217 149)(76 85 218 150)(77 86 219 151)(78 87 220 152)(79 88 221 153)(80 89 222 154)(81 90 223 155)(82 91 224 156)(83 92 197 157)(84 93 198 158)
(1 102 118 153)(2 168 119 89)(3 104 120 155)(4 142 121 91)(5 106 122 157)(6 144 123 93)(7 108 124 159)(8 146 125 95)(9 110 126 161)(10 148 127 97)(11 112 128 163)(12 150 129 99)(13 86 130 165)(14 152 131 101)(15 88 132 167)(16 154 133 103)(17 90 134 141)(18 156 135 105)(19 92 136 143)(20 158 137 107)(21 94 138 145)(22 160 139 109)(23 96 140 147)(24 162 113 111)(25 98 114 149)(26 164 115 85)(27 100 116 151)(28 166 117 87)(29 216 194 60)(30 75 195 203)(31 218 196 62)(32 77 169 205)(33 220 170 64)(34 79 171 207)(35 222 172 66)(36 81 173 209)(37 224 174 68)(38 83 175 211)(39 198 176 70)(40 57 177 213)(41 200 178 72)(42 59 179 215)(43 202 180 74)(44 61 181 217)(45 204 182 76)(46 63 183 219)(47 206 184 78)(48 65 185 221)(49 208 186 80)(50 67 187 223)(51 210 188 82)(52 69 189 197)(53 212 190 84)(54 71 191 199)(55 214 192 58)(56 73 193 201)
(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)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196)(197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224)
(1 117 15 131)(2 130 16 116)(3 115 17 129)(4 128 18 114)(5 113 19 127)(6 126 20 140)(7 139 21 125)(8 124 22 138)(9 137 23 123)(10 122 24 136)(11 135 25 121)(12 120 26 134)(13 133 27 119)(14 118 28 132)(29 189 43 175)(30 174 44 188)(31 187 45 173)(32 172 46 186)(33 185 47 171)(34 170 48 184)(35 183 49 169)(36 196 50 182)(37 181 51 195)(38 194 52 180)(39 179 53 193)(40 192 54 178)(41 177 55 191)(42 190 56 176)(57 214 71 200)(58 199 72 213)(59 212 73 198)(60 197 74 211)(61 210 75 224)(62 223 76 209)(63 208 77 222)(64 221 78 207)(65 206 79 220)(66 219 80 205)(67 204 81 218)(68 217 82 203)(69 202 83 216)(70 215 84 201)(85 141 99 155)(86 154 100 168)(87 167 101 153)(88 152 102 166)(89 165 103 151)(90 150 104 164)(91 163 105 149)(92 148 106 162)(93 161 107 147)(94 146 108 160)(95 159 109 145)(96 144 110 158)(97 157 111 143)(98 142 112 156)
G:=sub<Sym(224)| (1,171,132,48)(2,172,133,49)(3,173,134,50)(4,174,135,51)(5,175,136,52)(6,176,137,53)(7,177,138,54)(8,178,139,55)(9,179,140,56)(10,180,113,29)(11,181,114,30)(12,182,115,31)(13,183,116,32)(14,184,117,33)(15,185,118,34)(16,186,119,35)(17,187,120,36)(18,188,121,37)(19,189,122,38)(20,190,123,39)(21,191,124,40)(22,192,125,41)(23,193,126,42)(24,194,127,43)(25,195,128,44)(26,196,129,45)(27,169,130,46)(28,170,131,47)(57,94,199,159)(58,95,200,160)(59,96,201,161)(60,97,202,162)(61,98,203,163)(62,99,204,164)(63,100,205,165)(64,101,206,166)(65,102,207,167)(66,103,208,168)(67,104,209,141)(68,105,210,142)(69,106,211,143)(70,107,212,144)(71,108,213,145)(72,109,214,146)(73,110,215,147)(74,111,216,148)(75,112,217,149)(76,85,218,150)(77,86,219,151)(78,87,220,152)(79,88,221,153)(80,89,222,154)(81,90,223,155)(82,91,224,156)(83,92,197,157)(84,93,198,158), (1,102,118,153)(2,168,119,89)(3,104,120,155)(4,142,121,91)(5,106,122,157)(6,144,123,93)(7,108,124,159)(8,146,125,95)(9,110,126,161)(10,148,127,97)(11,112,128,163)(12,150,129,99)(13,86,130,165)(14,152,131,101)(15,88,132,167)(16,154,133,103)(17,90,134,141)(18,156,135,105)(19,92,136,143)(20,158,137,107)(21,94,138,145)(22,160,139,109)(23,96,140,147)(24,162,113,111)(25,98,114,149)(26,164,115,85)(27,100,116,151)(28,166,117,87)(29,216,194,60)(30,75,195,203)(31,218,196,62)(32,77,169,205)(33,220,170,64)(34,79,171,207)(35,222,172,66)(36,81,173,209)(37,224,174,68)(38,83,175,211)(39,198,176,70)(40,57,177,213)(41,200,178,72)(42,59,179,215)(43,202,180,74)(44,61,181,217)(45,204,182,76)(46,63,183,219)(47,206,184,78)(48,65,185,221)(49,208,186,80)(50,67,187,223)(51,210,188,82)(52,69,189,197)(53,212,190,84)(54,71,191,199)(55,214,192,58)(56,73,193,201), (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)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,117,15,131)(2,130,16,116)(3,115,17,129)(4,128,18,114)(5,113,19,127)(6,126,20,140)(7,139,21,125)(8,124,22,138)(9,137,23,123)(10,122,24,136)(11,135,25,121)(12,120,26,134)(13,133,27,119)(14,118,28,132)(29,189,43,175)(30,174,44,188)(31,187,45,173)(32,172,46,186)(33,185,47,171)(34,170,48,184)(35,183,49,169)(36,196,50,182)(37,181,51,195)(38,194,52,180)(39,179,53,193)(40,192,54,178)(41,177,55,191)(42,190,56,176)(57,214,71,200)(58,199,72,213)(59,212,73,198)(60,197,74,211)(61,210,75,224)(62,223,76,209)(63,208,77,222)(64,221,78,207)(65,206,79,220)(66,219,80,205)(67,204,81,218)(68,217,82,203)(69,202,83,216)(70,215,84,201)(85,141,99,155)(86,154,100,168)(87,167,101,153)(88,152,102,166)(89,165,103,151)(90,150,104,164)(91,163,105,149)(92,148,106,162)(93,161,107,147)(94,146,108,160)(95,159,109,145)(96,144,110,158)(97,157,111,143)(98,142,112,156)>;
G:=Group( (1,171,132,48)(2,172,133,49)(3,173,134,50)(4,174,135,51)(5,175,136,52)(6,176,137,53)(7,177,138,54)(8,178,139,55)(9,179,140,56)(10,180,113,29)(11,181,114,30)(12,182,115,31)(13,183,116,32)(14,184,117,33)(15,185,118,34)(16,186,119,35)(17,187,120,36)(18,188,121,37)(19,189,122,38)(20,190,123,39)(21,191,124,40)(22,192,125,41)(23,193,126,42)(24,194,127,43)(25,195,128,44)(26,196,129,45)(27,169,130,46)(28,170,131,47)(57,94,199,159)(58,95,200,160)(59,96,201,161)(60,97,202,162)(61,98,203,163)(62,99,204,164)(63,100,205,165)(64,101,206,166)(65,102,207,167)(66,103,208,168)(67,104,209,141)(68,105,210,142)(69,106,211,143)(70,107,212,144)(71,108,213,145)(72,109,214,146)(73,110,215,147)(74,111,216,148)(75,112,217,149)(76,85,218,150)(77,86,219,151)(78,87,220,152)(79,88,221,153)(80,89,222,154)(81,90,223,155)(82,91,224,156)(83,92,197,157)(84,93,198,158), (1,102,118,153)(2,168,119,89)(3,104,120,155)(4,142,121,91)(5,106,122,157)(6,144,123,93)(7,108,124,159)(8,146,125,95)(9,110,126,161)(10,148,127,97)(11,112,128,163)(12,150,129,99)(13,86,130,165)(14,152,131,101)(15,88,132,167)(16,154,133,103)(17,90,134,141)(18,156,135,105)(19,92,136,143)(20,158,137,107)(21,94,138,145)(22,160,139,109)(23,96,140,147)(24,162,113,111)(25,98,114,149)(26,164,115,85)(27,100,116,151)(28,166,117,87)(29,216,194,60)(30,75,195,203)(31,218,196,62)(32,77,169,205)(33,220,170,64)(34,79,171,207)(35,222,172,66)(36,81,173,209)(37,224,174,68)(38,83,175,211)(39,198,176,70)(40,57,177,213)(41,200,178,72)(42,59,179,215)(43,202,180,74)(44,61,181,217)(45,204,182,76)(46,63,183,219)(47,206,184,78)(48,65,185,221)(49,208,186,80)(50,67,187,223)(51,210,188,82)(52,69,189,197)(53,212,190,84)(54,71,191,199)(55,214,192,58)(56,73,193,201), (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)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,117,15,131)(2,130,16,116)(3,115,17,129)(4,128,18,114)(5,113,19,127)(6,126,20,140)(7,139,21,125)(8,124,22,138)(9,137,23,123)(10,122,24,136)(11,135,25,121)(12,120,26,134)(13,133,27,119)(14,118,28,132)(29,189,43,175)(30,174,44,188)(31,187,45,173)(32,172,46,186)(33,185,47,171)(34,170,48,184)(35,183,49,169)(36,196,50,182)(37,181,51,195)(38,194,52,180)(39,179,53,193)(40,192,54,178)(41,177,55,191)(42,190,56,176)(57,214,71,200)(58,199,72,213)(59,212,73,198)(60,197,74,211)(61,210,75,224)(62,223,76,209)(63,208,77,222)(64,221,78,207)(65,206,79,220)(66,219,80,205)(67,204,81,218)(68,217,82,203)(69,202,83,216)(70,215,84,201)(85,141,99,155)(86,154,100,168)(87,167,101,153)(88,152,102,166)(89,165,103,151)(90,150,104,164)(91,163,105,149)(92,148,106,162)(93,161,107,147)(94,146,108,160)(95,159,109,145)(96,144,110,158)(97,157,111,143)(98,142,112,156) );
G=PermutationGroup([[(1,171,132,48),(2,172,133,49),(3,173,134,50),(4,174,135,51),(5,175,136,52),(6,176,137,53),(7,177,138,54),(8,178,139,55),(9,179,140,56),(10,180,113,29),(11,181,114,30),(12,182,115,31),(13,183,116,32),(14,184,117,33),(15,185,118,34),(16,186,119,35),(17,187,120,36),(18,188,121,37),(19,189,122,38),(20,190,123,39),(21,191,124,40),(22,192,125,41),(23,193,126,42),(24,194,127,43),(25,195,128,44),(26,196,129,45),(27,169,130,46),(28,170,131,47),(57,94,199,159),(58,95,200,160),(59,96,201,161),(60,97,202,162),(61,98,203,163),(62,99,204,164),(63,100,205,165),(64,101,206,166),(65,102,207,167),(66,103,208,168),(67,104,209,141),(68,105,210,142),(69,106,211,143),(70,107,212,144),(71,108,213,145),(72,109,214,146),(73,110,215,147),(74,111,216,148),(75,112,217,149),(76,85,218,150),(77,86,219,151),(78,87,220,152),(79,88,221,153),(80,89,222,154),(81,90,223,155),(82,91,224,156),(83,92,197,157),(84,93,198,158)], [(1,102,118,153),(2,168,119,89),(3,104,120,155),(4,142,121,91),(5,106,122,157),(6,144,123,93),(7,108,124,159),(8,146,125,95),(9,110,126,161),(10,148,127,97),(11,112,128,163),(12,150,129,99),(13,86,130,165),(14,152,131,101),(15,88,132,167),(16,154,133,103),(17,90,134,141),(18,156,135,105),(19,92,136,143),(20,158,137,107),(21,94,138,145),(22,160,139,109),(23,96,140,147),(24,162,113,111),(25,98,114,149),(26,164,115,85),(27,100,116,151),(28,166,117,87),(29,216,194,60),(30,75,195,203),(31,218,196,62),(32,77,169,205),(33,220,170,64),(34,79,171,207),(35,222,172,66),(36,81,173,209),(37,224,174,68),(38,83,175,211),(39,198,176,70),(40,57,177,213),(41,200,178,72),(42,59,179,215),(43,202,180,74),(44,61,181,217),(45,204,182,76),(46,63,183,219),(47,206,184,78),(48,65,185,221),(49,208,186,80),(50,67,187,223),(51,210,188,82),(52,69,189,197),(53,212,190,84),(54,71,191,199),(55,214,192,58),(56,73,193,201)], [(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),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196),(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,117,15,131),(2,130,16,116),(3,115,17,129),(4,128,18,114),(5,113,19,127),(6,126,20,140),(7,139,21,125),(8,124,22,138),(9,137,23,123),(10,122,24,136),(11,135,25,121),(12,120,26,134),(13,133,27,119),(14,118,28,132),(29,189,43,175),(30,174,44,188),(31,187,45,173),(32,172,46,186),(33,185,47,171),(34,170,48,184),(35,183,49,169),(36,196,50,182),(37,181,51,195),(38,194,52,180),(39,179,53,193),(40,192,54,178),(41,177,55,191),(42,190,56,176),(57,214,71,200),(58,199,72,213),(59,212,73,198),(60,197,74,211),(61,210,75,224),(62,223,76,209),(63,208,77,222),(64,221,78,207),(65,206,79,220),(66,219,80,205),(67,204,81,218),(68,217,82,203),(69,202,83,216),(70,215,84,201),(85,141,99,155),(86,154,100,168),(87,167,101,153),(88,152,102,166),(89,165,103,151),(90,150,104,164),(91,163,105,149),(92,148,106,162),(93,161,107,147),(94,146,108,160),(95,159,109,145),(96,144,110,158),(97,157,111,143),(98,142,112,156)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | ··· | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 14 | 14 | 28 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | C4○D28 | D7×C4○D4 |
| kernel | C42.93D14 | C4×Dic14 | D7×C42 | C42⋊D7 | C4×D28 | C23.D14 | D14.D4 | D14⋊D4 | Dic7.D4 | Dic7.Q8 | D14.5D4 | D14⋊Q8 | C4⋊C4⋊D7 | C4×C7⋊D4 | C7×C42⋊C2 | C42⋊C2 | Dic7 | C28 | D14 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 3 | 4 | 4 | 4 | 6 | 6 | 6 | 3 | 24 | 12 |
Matrix representation of C42.93D14 ►in GL4(𝔽29) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 17 |
| 22 | 24 | 0 | 0 |
| 10 | 7 | 0 | 0 |
| 0 | 0 | 19 | 12 |
| 0 | 0 | 23 | 10 |
| 2 | 19 | 0 | 0 |
| 20 | 1 | 0 | 0 |
| 0 | 0 | 10 | 27 |
| 0 | 0 | 6 | 19 |
| 13 | 13 | 0 | 0 |
| 7 | 16 | 0 | 0 |
| 0 | 0 | 19 | 2 |
| 0 | 0 | 23 | 10 |
G:=sub<GL(4,GF(29))| [1,0,0,0,0,1,0,0,0,0,17,0,0,0,0,17],[22,10,0,0,24,7,0,0,0,0,19,23,0,0,12,10],[2,20,0,0,19,1,0,0,0,0,10,6,0,0,27,19],[13,7,0,0,13,16,0,0,0,0,19,23,0,0,2,10] >;
C42.93D14 in GAP, Magma, Sage, TeX
C_4^2._{93}D_{14} % in TeX
G:=Group("C4^2.93D14"); // GroupNames label
G:=SmallGroup(448,981);
// by ID
G=gap.SmallGroup(448,981);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,100,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=a^2*b,d*b*d^-1=b^-1,d*c*d^-1=c^13>;
// generators/relations