metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4.Q8⋊10D7, C4⋊C4.41D14, D14⋊C8.14C2, (C2×C8).140D14, C4.75(C4○D28), C28.32(C4○D4), C14.57(C4○D8), C14.Q16⋊17C2, C28.Q8⋊17C2, D14⋊2Q8.5C2, (C22×D7).26D4, C22.219(D4×D7), C28.44D4⋊32C2, (C2×C28).283C23, (C2×C56).287C22, C4.27(Q8⋊2D7), (C2×Dic7).164D4, C7⋊4(C23.20D4), C2.24(SD16⋊D7), C14.43(C8.C22), C4⋊Dic7.113C22, C2.24(SD16⋊3D7), C2.14(D14.5D4), (C2×Dic14).84C22, C14.44(C22.D4), (C7×C4.Q8)⋊18C2, C4⋊C4⋊7D7.6C2, (C2×C7⋊C8).60C22, (C2×C4×D7).35C22, (C2×C14).288(C2×D4), (C7×C4⋊C4).76C22, (C2×C4).386(C22×D7), SmallGroup(448,401)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4.(C4○D28)
G = < a,b,c,d | a4=b4=1, c14=a2b2, d2=a2, bab-1=cac-1=dad-1=a-1, cbc-1=ab, dbd-1=a-1b, dcd-1=b2c13 >
Subgroups: 492 in 96 conjugacy classes, 37 normal (all characteristic)
C1, C2 [×3], C2, C4 [×2], C4 [×5], C22, C22 [×3], C7, C8 [×2], C2×C4, C2×C4 [×7], Q8 [×2], C23, D7, C14 [×3], C42, C22⋊C4 [×2], C4⋊C4 [×2], C4⋊C4 [×2], C2×C8, C2×C8, C22×C4, C2×Q8, Dic7 [×3], C28 [×2], C28 [×2], D14 [×3], C2×C14, C22⋊C8, Q8⋊C4 [×2], C4.Q8, C2.D8, C42⋊C2, C22⋊Q8, C7⋊C8, C56, Dic14 [×2], C4×D7 [×2], C2×Dic7, C2×Dic7 [×2], C2×C28, C2×C28 [×2], C22×D7, C23.20D4, C2×C7⋊C8, C4×Dic7, C4⋊Dic7, C4⋊Dic7, D14⋊C4 [×2], C7×C4⋊C4 [×2], C2×C56, C2×Dic14, C2×C4×D7, C28.Q8, C14.Q16, C28.44D4, D14⋊C8, C7×C4.Q8, C4⋊C4⋊7D7, D14⋊2Q8, C4.(C4○D28)
Quotients: C1, C2 [×7], C22 [×7], D4 [×2], C23, D7, C2×D4, C4○D4 [×2], D14 [×3], C22.D4, C4○D8, C8.C22, C22×D7, C23.20D4, C4○D28, D4×D7, Q8⋊2D7, D14.5D4, SD16⋊D7, SD16⋊3D7, C4.(C4○D28)
►On 224 points
Generators in S224
(1 58 137 92)(2 93 138 59)(3 60 139 94)(4 95 140 61)(5 62 113 96)(6 97 114 63)(7 64 115 98)(8 99 116 65)(9 66 117 100)(10 101 118 67)(11 68 119 102)(12 103 120 69)(13 70 121 104)(14 105 122 71)(15 72 123 106)(16 107 124 73)(17 74 125 108)(18 109 126 75)(19 76 127 110)(20 111 128 77)(21 78 129 112)(22 85 130 79)(23 80 131 86)(24 87 132 81)(25 82 133 88)(26 89 134 83)(27 84 135 90)(28 91 136 57)(29 148 203 186)(30 187 204 149)(31 150 205 188)(32 189 206 151)(33 152 207 190)(34 191 208 153)(35 154 209 192)(36 193 210 155)(37 156 211 194)(38 195 212 157)(39 158 213 196)(40 169 214 159)(41 160 215 170)(42 171 216 161)(43 162 217 172)(44 173 218 163)(45 164 219 174)(46 175 220 165)(47 166 221 176)(48 177 222 167)(49 168 223 178)(50 179 224 141)(51 142 197 180)(52 181 198 143)(53 144 199 182)(54 183 200 145)(55 146 201 184)(56 185 202 147)
(1 217 123 29)(2 163 124 187)(3 219 125 31)(4 165 126 189)(5 221 127 33)(6 167 128 191)(7 223 129 35)(8 141 130 193)(9 197 131 37)(10 143 132 195)(11 199 133 39)(12 145 134 169)(13 201 135 41)(14 147 136 171)(15 203 137 43)(16 149 138 173)(17 205 139 45)(18 151 140 175)(19 207 113 47)(20 153 114 177)(21 209 115 49)(22 155 116 179)(23 211 117 51)(24 157 118 181)(25 213 119 53)(26 159 120 183)(27 215 121 55)(28 161 122 185)(30 93 218 73)(32 95 220 75)(34 97 222 77)(36 99 224 79)(38 101 198 81)(40 103 200 83)(42 105 202 57)(44 107 204 59)(46 109 206 61)(48 111 208 63)(50 85 210 65)(52 87 212 67)(54 89 214 69)(56 91 216 71)(58 162 106 186)(60 164 108 188)(62 166 110 190)(64 168 112 192)(66 142 86 194)(68 144 88 196)(70 146 90 170)(72 148 92 172)(74 150 94 174)(76 152 96 176)(78 154 98 178)(80 156 100 180)(82 158 102 182)(84 160 104 184)
(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)
(1 136 137 28)(2 27 138 135)(3 134 139 26)(4 25 140 133)(5 132 113 24)(6 23 114 131)(7 130 115 22)(8 21 116 129)(9 128 117 20)(10 19 118 127)(11 126 119 18)(12 17 120 125)(13 124 121 16)(14 15 122 123)(29 56 203 202)(30 201 204 55)(31 54 205 200)(32 199 206 53)(33 52 207 198)(34 197 208 51)(35 50 209 224)(36 223 210 49)(37 48 211 222)(38 221 212 47)(39 46 213 220)(40 219 214 45)(41 44 215 218)(42 217 216 43)(57 58 91 92)(59 84 93 90)(60 89 94 83)(61 82 95 88)(62 87 96 81)(63 80 97 86)(64 85 98 79)(65 78 99 112)(66 111 100 77)(67 76 101 110)(68 109 102 75)(69 74 103 108)(70 107 104 73)(71 72 105 106)(141 192 179 154)(142 153 180 191)(143 190 181 152)(144 151 182 189)(145 188 183 150)(146 149 184 187)(147 186 185 148)(155 178 193 168)(156 167 194 177)(157 176 195 166)(158 165 196 175)(159 174 169 164)(160 163 170 173)(161 172 171 162)
G:=sub<Sym(224)| (1,58,137,92)(2,93,138,59)(3,60,139,94)(4,95,140,61)(5,62,113,96)(6,97,114,63)(7,64,115,98)(8,99,116,65)(9,66,117,100)(10,101,118,67)(11,68,119,102)(12,103,120,69)(13,70,121,104)(14,105,122,71)(15,72,123,106)(16,107,124,73)(17,74,125,108)(18,109,126,75)(19,76,127,110)(20,111,128,77)(21,78,129,112)(22,85,130,79)(23,80,131,86)(24,87,132,81)(25,82,133,88)(26,89,134,83)(27,84,135,90)(28,91,136,57)(29,148,203,186)(30,187,204,149)(31,150,205,188)(32,189,206,151)(33,152,207,190)(34,191,208,153)(35,154,209,192)(36,193,210,155)(37,156,211,194)(38,195,212,157)(39,158,213,196)(40,169,214,159)(41,160,215,170)(42,171,216,161)(43,162,217,172)(44,173,218,163)(45,164,219,174)(46,175,220,165)(47,166,221,176)(48,177,222,167)(49,168,223,178)(50,179,224,141)(51,142,197,180)(52,181,198,143)(53,144,199,182)(54,183,200,145)(55,146,201,184)(56,185,202,147), (1,217,123,29)(2,163,124,187)(3,219,125,31)(4,165,126,189)(5,221,127,33)(6,167,128,191)(7,223,129,35)(8,141,130,193)(9,197,131,37)(10,143,132,195)(11,199,133,39)(12,145,134,169)(13,201,135,41)(14,147,136,171)(15,203,137,43)(16,149,138,173)(17,205,139,45)(18,151,140,175)(19,207,113,47)(20,153,114,177)(21,209,115,49)(22,155,116,179)(23,211,117,51)(24,157,118,181)(25,213,119,53)(26,159,120,183)(27,215,121,55)(28,161,122,185)(30,93,218,73)(32,95,220,75)(34,97,222,77)(36,99,224,79)(38,101,198,81)(40,103,200,83)(42,105,202,57)(44,107,204,59)(46,109,206,61)(48,111,208,63)(50,85,210,65)(52,87,212,67)(54,89,214,69)(56,91,216,71)(58,162,106,186)(60,164,108,188)(62,166,110,190)(64,168,112,192)(66,142,86,194)(68,144,88,196)(70,146,90,170)(72,148,92,172)(74,150,94,174)(76,152,96,176)(78,154,98,178)(80,156,100,180)(82,158,102,182)(84,160,104,184), (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), (1,136,137,28)(2,27,138,135)(3,134,139,26)(4,25,140,133)(5,132,113,24)(6,23,114,131)(7,130,115,22)(8,21,116,129)(9,128,117,20)(10,19,118,127)(11,126,119,18)(12,17,120,125)(13,124,121,16)(14,15,122,123)(29,56,203,202)(30,201,204,55)(31,54,205,200)(32,199,206,53)(33,52,207,198)(34,197,208,51)(35,50,209,224)(36,223,210,49)(37,48,211,222)(38,221,212,47)(39,46,213,220)(40,219,214,45)(41,44,215,218)(42,217,216,43)(57,58,91,92)(59,84,93,90)(60,89,94,83)(61,82,95,88)(62,87,96,81)(63,80,97,86)(64,85,98,79)(65,78,99,112)(66,111,100,77)(67,76,101,110)(68,109,102,75)(69,74,103,108)(70,107,104,73)(71,72,105,106)(141,192,179,154)(142,153,180,191)(143,190,181,152)(144,151,182,189)(145,188,183,150)(146,149,184,187)(147,186,185,148)(155,178,193,168)(156,167,194,177)(157,176,195,166)(158,165,196,175)(159,174,169,164)(160,163,170,173)(161,172,171,162)>;
G:=Group( (1,58,137,92)(2,93,138,59)(3,60,139,94)(4,95,140,61)(5,62,113,96)(6,97,114,63)(7,64,115,98)(8,99,116,65)(9,66,117,100)(10,101,118,67)(11,68,119,102)(12,103,120,69)(13,70,121,104)(14,105,122,71)(15,72,123,106)(16,107,124,73)(17,74,125,108)(18,109,126,75)(19,76,127,110)(20,111,128,77)(21,78,129,112)(22,85,130,79)(23,80,131,86)(24,87,132,81)(25,82,133,88)(26,89,134,83)(27,84,135,90)(28,91,136,57)(29,148,203,186)(30,187,204,149)(31,150,205,188)(32,189,206,151)(33,152,207,190)(34,191,208,153)(35,154,209,192)(36,193,210,155)(37,156,211,194)(38,195,212,157)(39,158,213,196)(40,169,214,159)(41,160,215,170)(42,171,216,161)(43,162,217,172)(44,173,218,163)(45,164,219,174)(46,175,220,165)(47,166,221,176)(48,177,222,167)(49,168,223,178)(50,179,224,141)(51,142,197,180)(52,181,198,143)(53,144,199,182)(54,183,200,145)(55,146,201,184)(56,185,202,147), (1,217,123,29)(2,163,124,187)(3,219,125,31)(4,165,126,189)(5,221,127,33)(6,167,128,191)(7,223,129,35)(8,141,130,193)(9,197,131,37)(10,143,132,195)(11,199,133,39)(12,145,134,169)(13,201,135,41)(14,147,136,171)(15,203,137,43)(16,149,138,173)(17,205,139,45)(18,151,140,175)(19,207,113,47)(20,153,114,177)(21,209,115,49)(22,155,116,179)(23,211,117,51)(24,157,118,181)(25,213,119,53)(26,159,120,183)(27,215,121,55)(28,161,122,185)(30,93,218,73)(32,95,220,75)(34,97,222,77)(36,99,224,79)(38,101,198,81)(40,103,200,83)(42,105,202,57)(44,107,204,59)(46,109,206,61)(48,111,208,63)(50,85,210,65)(52,87,212,67)(54,89,214,69)(56,91,216,71)(58,162,106,186)(60,164,108,188)(62,166,110,190)(64,168,112,192)(66,142,86,194)(68,144,88,196)(70,146,90,170)(72,148,92,172)(74,150,94,174)(76,152,96,176)(78,154,98,178)(80,156,100,180)(82,158,102,182)(84,160,104,184), (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), (1,136,137,28)(2,27,138,135)(3,134,139,26)(4,25,140,133)(5,132,113,24)(6,23,114,131)(7,130,115,22)(8,21,116,129)(9,128,117,20)(10,19,118,127)(11,126,119,18)(12,17,120,125)(13,124,121,16)(14,15,122,123)(29,56,203,202)(30,201,204,55)(31,54,205,200)(32,199,206,53)(33,52,207,198)(34,197,208,51)(35,50,209,224)(36,223,210,49)(37,48,211,222)(38,221,212,47)(39,46,213,220)(40,219,214,45)(41,44,215,218)(42,217,216,43)(57,58,91,92)(59,84,93,90)(60,89,94,83)(61,82,95,88)(62,87,96,81)(63,80,97,86)(64,85,98,79)(65,78,99,112)(66,111,100,77)(67,76,101,110)(68,109,102,75)(69,74,103,108)(70,107,104,73)(71,72,105,106)(141,192,179,154)(142,153,180,191)(143,190,181,152)(144,151,182,189)(145,188,183,150)(146,149,184,187)(147,186,185,148)(155,178,193,168)(156,167,194,177)(157,176,195,166)(158,165,196,175)(159,174,169,164)(160,163,170,173)(161,172,171,162) );
G=PermutationGroup([(1,58,137,92),(2,93,138,59),(3,60,139,94),(4,95,140,61),(5,62,113,96),(6,97,114,63),(7,64,115,98),(8,99,116,65),(9,66,117,100),(10,101,118,67),(11,68,119,102),(12,103,120,69),(13,70,121,104),(14,105,122,71),(15,72,123,106),(16,107,124,73),(17,74,125,108),(18,109,126,75),(19,76,127,110),(20,111,128,77),(21,78,129,112),(22,85,130,79),(23,80,131,86),(24,87,132,81),(25,82,133,88),(26,89,134,83),(27,84,135,90),(28,91,136,57),(29,148,203,186),(30,187,204,149),(31,150,205,188),(32,189,206,151),(33,152,207,190),(34,191,208,153),(35,154,209,192),(36,193,210,155),(37,156,211,194),(38,195,212,157),(39,158,213,196),(40,169,214,159),(41,160,215,170),(42,171,216,161),(43,162,217,172),(44,173,218,163),(45,164,219,174),(46,175,220,165),(47,166,221,176),(48,177,222,167),(49,168,223,178),(50,179,224,141),(51,142,197,180),(52,181,198,143),(53,144,199,182),(54,183,200,145),(55,146,201,184),(56,185,202,147)], [(1,217,123,29),(2,163,124,187),(3,219,125,31),(4,165,126,189),(5,221,127,33),(6,167,128,191),(7,223,129,35),(8,141,130,193),(9,197,131,37),(10,143,132,195),(11,199,133,39),(12,145,134,169),(13,201,135,41),(14,147,136,171),(15,203,137,43),(16,149,138,173),(17,205,139,45),(18,151,140,175),(19,207,113,47),(20,153,114,177),(21,209,115,49),(22,155,116,179),(23,211,117,51),(24,157,118,181),(25,213,119,53),(26,159,120,183),(27,215,121,55),(28,161,122,185),(30,93,218,73),(32,95,220,75),(34,97,222,77),(36,99,224,79),(38,101,198,81),(40,103,200,83),(42,105,202,57),(44,107,204,59),(46,109,206,61),(48,111,208,63),(50,85,210,65),(52,87,212,67),(54,89,214,69),(56,91,216,71),(58,162,106,186),(60,164,108,188),(62,166,110,190),(64,168,112,192),(66,142,86,194),(68,144,88,196),(70,146,90,170),(72,148,92,172),(74,150,94,174),(76,152,96,176),(78,154,98,178),(80,156,100,180),(82,158,102,182),(84,160,104,184)], [(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)], [(1,136,137,28),(2,27,138,135),(3,134,139,26),(4,25,140,133),(5,132,113,24),(6,23,114,131),(7,130,115,22),(8,21,116,129),(9,128,117,20),(10,19,118,127),(11,126,119,18),(12,17,120,125),(13,124,121,16),(14,15,122,123),(29,56,203,202),(30,201,204,55),(31,54,205,200),(32,199,206,53),(33,52,207,198),(34,197,208,51),(35,50,209,224),(36,223,210,49),(37,48,211,222),(38,221,212,47),(39,46,213,220),(40,219,214,45),(41,44,215,218),(42,217,216,43),(57,58,91,92),(59,84,93,90),(60,89,94,83),(61,82,95,88),(62,87,96,81),(63,80,97,86),(64,85,98,79),(65,78,99,112),(66,111,100,77),(67,76,101,110),(68,109,102,75),(69,74,103,108),(70,107,104,73),(71,72,105,106),(141,192,179,154),(142,153,180,191),(143,190,181,152),(144,151,182,189),(145,188,183,150),(146,149,184,187),(147,186,185,148),(155,178,193,168),(156,167,194,177),(157,176,195,166),(158,165,196,175),(159,174,169,164),(160,163,170,173),(161,172,171,162)])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | + | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | C4○D8 | C4○D28 | C8.C22 | Q8⋊2D7 | D4×D7 | SD16⋊D7 | SD16⋊3D7 |
| kernel | C4.(C4○D28) | C28.Q8 | C14.Q16 | C28.44D4 | D14⋊C8 | C7×C4.Q8 | C4⋊C4⋊7D7 | D14⋊2Q8 | C2×Dic7 | C22×D7 | C4.Q8 | C28 | C4⋊C4 | C2×C8 | C14 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 6 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of C4.(C4○D28) ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 111 | 15 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 95 | 44 |
| 0 | 0 | 26 | 18 |
| 36 | 90 | 0 | 0 |
| 23 | 23 | 0 | 0 |
| 0 | 0 | 98 | 112 |
| 0 | 0 | 111 | 15 |
| 105 | 17 | 0 | 0 |
| 96 | 8 | 0 | 0 |
| 0 | 0 | 98 | 112 |
| 0 | 0 | 0 | 15 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,98,111,0,0,0,15],[15,0,0,0,0,15,0,0,0,0,95,26,0,0,44,18],[36,23,0,0,90,23,0,0,0,0,98,111,0,0,112,15],[105,96,0,0,17,8,0,0,0,0,98,0,0,0,112,15] >;
C4.(C4○D28) in GAP, Magma, Sage, TeX
C_4.(C_4\circ D_{28}) % in TeX
G:=Group("C4.(C4oD28)"); // GroupNames label
G:=SmallGroup(448,401);
// by ID
G=gap.SmallGroup(448,401);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,64,926,219,100,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2*b^2,d^2=a^2,b*a*b^-1=c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a*b,d*b*d^-1=a^-1*b,d*c*d^-1=b^2*c^13>;
// generators/relations