direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C7×C4⋊M4(2), C28⋊9M4(2), C42.11C28, C4⋊C8⋊11C14, (C4×C28).26C4, C4.75(D4×C14), C4⋊2(C7×M4(2)), C28.60(C4⋊C4), (C2×C28).74Q8, C4.22(Q8×C14), (C2×C28).416D4, C28.480(C2×D4), C28.128(C2×Q8), (C22×C4).15C28, C42.67(C2×C14), C23.31(C2×C28), (C22×C28).35C4, (C2×C42).14C14, C2.7(C14×M4(2)), (C2×C56).324C22, (C4×C28).351C22, (C2×C28).985C23, C14.50(C2×M4(2)), (C2×M4(2)).13C14, (C14×M4(2)).31C2, C22.43(C22×C28), (C22×C28).585C22, (C7×C4⋊C8)⋊30C2, C4.11(C7×C4⋊C4), C2.9(C14×C4⋊C4), (C2×C4×C28).37C2, C14.65(C2×C4⋊C4), (C2×C4).71(C7×D4), C22.7(C7×C4⋊C4), (C2×C4).16(C7×Q8), (C2×C4).73(C2×C28), (C2×C8).49(C2×C14), (C2×C14).24(C4⋊C4), (C2×C28).289(C2×C4), (C22×C14).117(C2×C4), (C2×C14).235(C22×C4), (C22×C4).114(C2×C14), (C2×C4).153(C22×C14), SmallGroup(448,831)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×C4⋊M4(2)
G = < a,b,c,d | a7=b4=c8=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd=c5 >
Subgroups: 162 in 126 conjugacy classes, 90 normal (26 characteristic)
C1, C2, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, C23, C14, C14, C14, C42, C42, C2×C8, M4(2), C22×C4, C22×C4, C28, C28, C28, C2×C14, C2×C14, C2×C14, C4⋊C8, C2×C42, C2×M4(2), C56, C2×C28, C2×C28, C2×C28, C22×C14, C4⋊M4(2), C4×C28, C4×C28, C2×C56, C7×M4(2), C22×C28, C22×C28, C7×C4⋊C8, C2×C4×C28, C14×M4(2), C7×C4⋊M4(2)
Quotients: C1, C2, C4, C22, C7, C2×C4, D4, Q8, C23, C14, C4⋊C4, M4(2), C22×C4, C2×D4, C2×Q8, C28, C2×C14, C2×C4⋊C4, C2×M4(2), C2×C28, C7×D4, C7×Q8, C22×C14, C4⋊M4(2), C7×C4⋊C4, C7×M4(2), C22×C28, D4×C14, Q8×C14, C14×C4⋊C4, C14×M4(2), C7×C4⋊M4(2)
►On 224 points
Generators in S224
(1 195 87 187 79 179 71)(2 196 88 188 80 180 72)(3 197 81 189 73 181 65)(4 198 82 190 74 182 66)(5 199 83 191 75 183 67)(6 200 84 192 76 184 68)(7 193 85 185 77 177 69)(8 194 86 186 78 178 70)(9 33 141 25 133 17 125)(10 34 142 26 134 18 126)(11 35 143 27 135 19 127)(12 36 144 28 136 20 128)(13 37 137 29 129 21 121)(14 38 138 30 130 22 122)(15 39 139 31 131 23 123)(16 40 140 32 132 24 124)(41 149 173 57 165 49 157)(42 150 174 58 166 50 158)(43 151 175 59 167 51 159)(44 152 176 60 168 52 160)(45 145 169 61 161 53 153)(46 146 170 62 162 54 154)(47 147 171 63 163 55 155)(48 148 172 64 164 56 156)(89 116 221 105 213 97 205)(90 117 222 106 214 98 206)(91 118 223 107 215 99 207)(92 119 224 108 216 100 208)(93 120 217 109 209 101 201)(94 113 218 110 210 102 202)(95 114 219 111 211 103 203)(96 115 220 112 212 104 204)
(1 89 13 147)(2 148 14 90)(3 91 15 149)(4 150 16 92)(5 93 9 151)(6 152 10 94)(7 95 11 145)(8 146 12 96)(17 159 183 101)(18 102 184 160)(19 153 177 103)(20 104 178 154)(21 155 179 97)(22 98 180 156)(23 157 181 99)(24 100 182 158)(25 167 191 109)(26 110 192 168)(27 161 185 111)(28 112 186 162)(29 163 187 105)(30 106 188 164)(31 165 189 107)(32 108 190 166)(33 175 199 120)(34 113 200 176)(35 169 193 114)(36 115 194 170)(37 171 195 116)(38 117 196 172)(39 173 197 118)(40 119 198 174)(41 65 207 123)(42 124 208 66)(43 67 201 125)(44 126 202 68)(45 69 203 127)(46 128 204 70)(47 71 205 121)(48 122 206 72)(49 73 215 131)(50 132 216 74)(51 75 209 133)(52 134 210 76)(53 77 211 135)(54 136 212 78)(55 79 213 129)(56 130 214 80)(57 81 223 139)(58 140 224 82)(59 83 217 141)(60 142 218 84)(61 85 219 143)(62 144 220 86)(63 87 221 137)(64 138 222 88)
(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 9)(2 14)(3 11)(4 16)(5 13)(6 10)(7 15)(8 12)(17 179)(18 184)(19 181)(20 178)(21 183)(22 180)(23 177)(24 182)(25 187)(26 192)(27 189)(28 186)(29 191)(30 188)(31 185)(32 190)(33 195)(34 200)(35 197)(36 194)(37 199)(38 196)(39 193)(40 198)(41 203)(42 208)(43 205)(44 202)(45 207)(46 204)(47 201)(48 206)(49 211)(50 216)(51 213)(52 210)(53 215)(54 212)(55 209)(56 214)(57 219)(58 224)(59 221)(60 218)(61 223)(62 220)(63 217)(64 222)(65 127)(66 124)(67 121)(68 126)(69 123)(70 128)(71 125)(72 122)(73 135)(74 132)(75 129)(76 134)(77 131)(78 136)(79 133)(80 130)(81 143)(82 140)(83 137)(84 142)(85 139)(86 144)(87 141)(88 138)(89 151)(90 148)(91 145)(92 150)(93 147)(94 152)(95 149)(96 146)(97 159)(98 156)(99 153)(100 158)(101 155)(102 160)(103 157)(104 154)(105 167)(106 164)(107 161)(108 166)(109 163)(110 168)(111 165)(112 162)(113 176)(114 173)(115 170)(116 175)(117 172)(118 169)(119 174)(120 171)
G:=sub<Sym(224)| (1,195,87,187,79,179,71)(2,196,88,188,80,180,72)(3,197,81,189,73,181,65)(4,198,82,190,74,182,66)(5,199,83,191,75,183,67)(6,200,84,192,76,184,68)(7,193,85,185,77,177,69)(8,194,86,186,78,178,70)(9,33,141,25,133,17,125)(10,34,142,26,134,18,126)(11,35,143,27,135,19,127)(12,36,144,28,136,20,128)(13,37,137,29,129,21,121)(14,38,138,30,130,22,122)(15,39,139,31,131,23,123)(16,40,140,32,132,24,124)(41,149,173,57,165,49,157)(42,150,174,58,166,50,158)(43,151,175,59,167,51,159)(44,152,176,60,168,52,160)(45,145,169,61,161,53,153)(46,146,170,62,162,54,154)(47,147,171,63,163,55,155)(48,148,172,64,164,56,156)(89,116,221,105,213,97,205)(90,117,222,106,214,98,206)(91,118,223,107,215,99,207)(92,119,224,108,216,100,208)(93,120,217,109,209,101,201)(94,113,218,110,210,102,202)(95,114,219,111,211,103,203)(96,115,220,112,212,104,204), (1,89,13,147)(2,148,14,90)(3,91,15,149)(4,150,16,92)(5,93,9,151)(6,152,10,94)(7,95,11,145)(8,146,12,96)(17,159,183,101)(18,102,184,160)(19,153,177,103)(20,104,178,154)(21,155,179,97)(22,98,180,156)(23,157,181,99)(24,100,182,158)(25,167,191,109)(26,110,192,168)(27,161,185,111)(28,112,186,162)(29,163,187,105)(30,106,188,164)(31,165,189,107)(32,108,190,166)(33,175,199,120)(34,113,200,176)(35,169,193,114)(36,115,194,170)(37,171,195,116)(38,117,196,172)(39,173,197,118)(40,119,198,174)(41,65,207,123)(42,124,208,66)(43,67,201,125)(44,126,202,68)(45,69,203,127)(46,128,204,70)(47,71,205,121)(48,122,206,72)(49,73,215,131)(50,132,216,74)(51,75,209,133)(52,134,210,76)(53,77,211,135)(54,136,212,78)(55,79,213,129)(56,130,214,80)(57,81,223,139)(58,140,224,82)(59,83,217,141)(60,142,218,84)(61,85,219,143)(62,144,220,86)(63,87,221,137)(64,138,222,88), (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), (1,9)(2,14)(3,11)(4,16)(5,13)(6,10)(7,15)(8,12)(17,179)(18,184)(19,181)(20,178)(21,183)(22,180)(23,177)(24,182)(25,187)(26,192)(27,189)(28,186)(29,191)(30,188)(31,185)(32,190)(33,195)(34,200)(35,197)(36,194)(37,199)(38,196)(39,193)(40,198)(41,203)(42,208)(43,205)(44,202)(45,207)(46,204)(47,201)(48,206)(49,211)(50,216)(51,213)(52,210)(53,215)(54,212)(55,209)(56,214)(57,219)(58,224)(59,221)(60,218)(61,223)(62,220)(63,217)(64,222)(65,127)(66,124)(67,121)(68,126)(69,123)(70,128)(71,125)(72,122)(73,135)(74,132)(75,129)(76,134)(77,131)(78,136)(79,133)(80,130)(81,143)(82,140)(83,137)(84,142)(85,139)(86,144)(87,141)(88,138)(89,151)(90,148)(91,145)(92,150)(93,147)(94,152)(95,149)(96,146)(97,159)(98,156)(99,153)(100,158)(101,155)(102,160)(103,157)(104,154)(105,167)(106,164)(107,161)(108,166)(109,163)(110,168)(111,165)(112,162)(113,176)(114,173)(115,170)(116,175)(117,172)(118,169)(119,174)(120,171)>;
G:=Group( (1,195,87,187,79,179,71)(2,196,88,188,80,180,72)(3,197,81,189,73,181,65)(4,198,82,190,74,182,66)(5,199,83,191,75,183,67)(6,200,84,192,76,184,68)(7,193,85,185,77,177,69)(8,194,86,186,78,178,70)(9,33,141,25,133,17,125)(10,34,142,26,134,18,126)(11,35,143,27,135,19,127)(12,36,144,28,136,20,128)(13,37,137,29,129,21,121)(14,38,138,30,130,22,122)(15,39,139,31,131,23,123)(16,40,140,32,132,24,124)(41,149,173,57,165,49,157)(42,150,174,58,166,50,158)(43,151,175,59,167,51,159)(44,152,176,60,168,52,160)(45,145,169,61,161,53,153)(46,146,170,62,162,54,154)(47,147,171,63,163,55,155)(48,148,172,64,164,56,156)(89,116,221,105,213,97,205)(90,117,222,106,214,98,206)(91,118,223,107,215,99,207)(92,119,224,108,216,100,208)(93,120,217,109,209,101,201)(94,113,218,110,210,102,202)(95,114,219,111,211,103,203)(96,115,220,112,212,104,204), (1,89,13,147)(2,148,14,90)(3,91,15,149)(4,150,16,92)(5,93,9,151)(6,152,10,94)(7,95,11,145)(8,146,12,96)(17,159,183,101)(18,102,184,160)(19,153,177,103)(20,104,178,154)(21,155,179,97)(22,98,180,156)(23,157,181,99)(24,100,182,158)(25,167,191,109)(26,110,192,168)(27,161,185,111)(28,112,186,162)(29,163,187,105)(30,106,188,164)(31,165,189,107)(32,108,190,166)(33,175,199,120)(34,113,200,176)(35,169,193,114)(36,115,194,170)(37,171,195,116)(38,117,196,172)(39,173,197,118)(40,119,198,174)(41,65,207,123)(42,124,208,66)(43,67,201,125)(44,126,202,68)(45,69,203,127)(46,128,204,70)(47,71,205,121)(48,122,206,72)(49,73,215,131)(50,132,216,74)(51,75,209,133)(52,134,210,76)(53,77,211,135)(54,136,212,78)(55,79,213,129)(56,130,214,80)(57,81,223,139)(58,140,224,82)(59,83,217,141)(60,142,218,84)(61,85,219,143)(62,144,220,86)(63,87,221,137)(64,138,222,88), (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), (1,9)(2,14)(3,11)(4,16)(5,13)(6,10)(7,15)(8,12)(17,179)(18,184)(19,181)(20,178)(21,183)(22,180)(23,177)(24,182)(25,187)(26,192)(27,189)(28,186)(29,191)(30,188)(31,185)(32,190)(33,195)(34,200)(35,197)(36,194)(37,199)(38,196)(39,193)(40,198)(41,203)(42,208)(43,205)(44,202)(45,207)(46,204)(47,201)(48,206)(49,211)(50,216)(51,213)(52,210)(53,215)(54,212)(55,209)(56,214)(57,219)(58,224)(59,221)(60,218)(61,223)(62,220)(63,217)(64,222)(65,127)(66,124)(67,121)(68,126)(69,123)(70,128)(71,125)(72,122)(73,135)(74,132)(75,129)(76,134)(77,131)(78,136)(79,133)(80,130)(81,143)(82,140)(83,137)(84,142)(85,139)(86,144)(87,141)(88,138)(89,151)(90,148)(91,145)(92,150)(93,147)(94,152)(95,149)(96,146)(97,159)(98,156)(99,153)(100,158)(101,155)(102,160)(103,157)(104,154)(105,167)(106,164)(107,161)(108,166)(109,163)(110,168)(111,165)(112,162)(113,176)(114,173)(115,170)(116,175)(117,172)(118,169)(119,174)(120,171) );
G=PermutationGroup([[(1,195,87,187,79,179,71),(2,196,88,188,80,180,72),(3,197,81,189,73,181,65),(4,198,82,190,74,182,66),(5,199,83,191,75,183,67),(6,200,84,192,76,184,68),(7,193,85,185,77,177,69),(8,194,86,186,78,178,70),(9,33,141,25,133,17,125),(10,34,142,26,134,18,126),(11,35,143,27,135,19,127),(12,36,144,28,136,20,128),(13,37,137,29,129,21,121),(14,38,138,30,130,22,122),(15,39,139,31,131,23,123),(16,40,140,32,132,24,124),(41,149,173,57,165,49,157),(42,150,174,58,166,50,158),(43,151,175,59,167,51,159),(44,152,176,60,168,52,160),(45,145,169,61,161,53,153),(46,146,170,62,162,54,154),(47,147,171,63,163,55,155),(48,148,172,64,164,56,156),(89,116,221,105,213,97,205),(90,117,222,106,214,98,206),(91,118,223,107,215,99,207),(92,119,224,108,216,100,208),(93,120,217,109,209,101,201),(94,113,218,110,210,102,202),(95,114,219,111,211,103,203),(96,115,220,112,212,104,204)], [(1,89,13,147),(2,148,14,90),(3,91,15,149),(4,150,16,92),(5,93,9,151),(6,152,10,94),(7,95,11,145),(8,146,12,96),(17,159,183,101),(18,102,184,160),(19,153,177,103),(20,104,178,154),(21,155,179,97),(22,98,180,156),(23,157,181,99),(24,100,182,158),(25,167,191,109),(26,110,192,168),(27,161,185,111),(28,112,186,162),(29,163,187,105),(30,106,188,164),(31,165,189,107),(32,108,190,166),(33,175,199,120),(34,113,200,176),(35,169,193,114),(36,115,194,170),(37,171,195,116),(38,117,196,172),(39,173,197,118),(40,119,198,174),(41,65,207,123),(42,124,208,66),(43,67,201,125),(44,126,202,68),(45,69,203,127),(46,128,204,70),(47,71,205,121),(48,122,206,72),(49,73,215,131),(50,132,216,74),(51,75,209,133),(52,134,210,76),(53,77,211,135),(54,136,212,78),(55,79,213,129),(56,130,214,80),(57,81,223,139),(58,140,224,82),(59,83,217,141),(60,142,218,84),(61,85,219,143),(62,144,220,86),(63,87,221,137),(64,138,222,88)], [(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)], [(1,9),(2,14),(3,11),(4,16),(5,13),(6,10),(7,15),(8,12),(17,179),(18,184),(19,181),(20,178),(21,183),(22,180),(23,177),(24,182),(25,187),(26,192),(27,189),(28,186),(29,191),(30,188),(31,185),(32,190),(33,195),(34,200),(35,197),(36,194),(37,199),(38,196),(39,193),(40,198),(41,203),(42,208),(43,205),(44,202),(45,207),(46,204),(47,201),(48,206),(49,211),(50,216),(51,213),(52,210),(53,215),(54,212),(55,209),(56,214),(57,219),(58,224),(59,221),(60,218),(61,223),(62,220),(63,217),(64,222),(65,127),(66,124),(67,121),(68,126),(69,123),(70,128),(71,125),(72,122),(73,135),(74,132),(75,129),(76,134),(77,131),(78,136),(79,133),(80,130),(81,143),(82,140),(83,137),(84,142),(85,139),(86,144),(87,141),(88,138),(89,151),(90,148),(91,145),(92,150),(93,147),(94,152),(95,149),(96,146),(97,159),(98,156),(99,153),(100,158),(101,155),(102,160),(103,157),(104,154),(105,167),(106,164),(107,161),(108,166),(109,163),(110,168),(111,165),(112,162),(113,176),(114,173),(115,170),(116,175),(117,172),(118,169),(119,174),(120,171)]])
196 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | ··· | 4N | 7A | ··· | 7F | 8A | ··· | 8H | 14A | ··· | 14R | 14S | ··· | 14AD | 28A | ··· | 28X | 28Y | ··· | 28CF | 56A | ··· | 56AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 4 | ··· | 4 | 1 | ··· | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | ||||||||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C7 | C14 | C14 | C14 | C28 | C28 | D4 | Q8 | M4(2) | C7×D4 | C7×Q8 | C7×M4(2) |
| kernel | C7×C4⋊M4(2) | C7×C4⋊C8 | C2×C4×C28 | C14×M4(2) | C4×C28 | C22×C28 | C4⋊M4(2) | C4⋊C8 | C2×C42 | C2×M4(2) | C42 | C22×C4 | C2×C28 | C2×C28 | C28 | C2×C4 | C2×C4 | C4 |
| # reps | 1 | 4 | 1 | 2 | 4 | 4 | 6 | 24 | 6 | 12 | 24 | 24 | 2 | 2 | 8 | 12 | 12 | 48 |
Matrix representation of C7×C4⋊M4(2) ►in GL4(𝔽113) generated by
| 30 | 0 | 0 | 0 |
| 0 | 30 | 0 | 0 |
| 0 | 0 | 16 | 0 |
| 0 | 0 | 0 | 16 |
| 1 | 112 | 0 | 0 |
| 2 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 98 | 15 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 46 | 2 |
| 0 | 0 | 23 | 67 |
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 46 | 1 |
G:=sub<GL(4,GF(113))| [30,0,0,0,0,30,0,0,0,0,16,0,0,0,0,16],[1,2,0,0,112,112,0,0,0,0,112,0,0,0,0,112],[98,0,0,0,15,15,0,0,0,0,46,23,0,0,2,67],[112,0,0,0,0,112,0,0,0,0,112,46,0,0,0,1] >;
C7×C4⋊M4(2) in GAP, Magma, Sage, TeX
C_7\times C_4\rtimes M_4(2)
% in TeX
G:=Group("C7xC4:M4(2)"); // GroupNames label
G:=SmallGroup(448,831);
// by ID
G=gap.SmallGroup(448,831);
# by ID
G:=PCGroup([7,-2,-2,-2,-7,-2,-2,-2,784,813,400,4790,124]);
// Polycyclic
G:=Group<a,b,c,d|a^7=b^4=c^8=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d=c^5>;
// generators/relations