metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.230D14, (C2×C28).285D4, (C2×C14).17Q16, C14.33(C2×Q16), C4.88(C4○D28), C14.Q16⋊25C2, C28.Q8⋊26C2, (C22×C4).96D14, C28.176(C4○D4), C14.85(C8⋊C22), (C2×C28).323C23, C28.55D4.3C2, C28.48D4.9C2, (C22×C14).188D4, C23.79(C7⋊D4), C7⋊4(C23.48D4), C22.5(C7⋊Q16), C2.7(D4.D14), C4⋊Dic7.132C22, (C22×C28).138C22, (C2×Dic14).96C22, C14.60(C22.D4), C2.10(C23.23D14), (C2×C4⋊C4).8D7, (C14×C4⋊C4).7C2, C2.5(C2×C7⋊Q16), (C2×C7⋊C8).83C22, (C2×C14).443(C2×D4), (C2×C4).33(C7⋊D4), (C7×C4⋊C4).261C22, (C2×C4).423(C22×D7), C22.132(C2×C7⋊D4), SmallGroup(448,504)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.230D14
G = < a,b,c,d | a4=b4=c14=1, d2=b2, bab-1=dad-1=a-1, ac=ca, bc=cb, dbd-1=ab, dcd-1=a2b2c-1 >
Subgroups: 388 in 104 conjugacy classes, 43 normal (25 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C22×C4, C22×C4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C22⋊C8, Q8⋊C4, C2.D8, C2×C4⋊C4, C22⋊Q8, C7⋊C8, Dic14, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.48D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C23.D7, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, C22×C28, C28.Q8, C14.Q16, C28.55D4, C28.48D4, C14×C4⋊C4, C4⋊C4.230D14
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, C4○D4, D14, C22.D4, C2×Q16, C8⋊C22, C7⋊D4, C22×D7, C23.48D4, C7⋊Q16, C4○D28, C2×C7⋊D4, C23.23D14, D4.D14, C2×C7⋊Q16, C4⋊C4.230D14
►On 224 points
Generators in S224
(1 205 8 198)(2 206 9 199)(3 207 10 200)(4 208 11 201)(5 209 12 202)(6 210 13 203)(7 197 14 204)(15 114 22 121)(16 115 23 122)(17 116 24 123)(18 117 25 124)(19 118 26 125)(20 119 27 126)(21 120 28 113)(29 178 145 217)(30 179 146 218)(31 180 147 219)(32 181 148 220)(33 182 149 221)(34 169 150 222)(35 170 151 223)(36 171 152 224)(37 172 153 211)(38 173 154 212)(39 174 141 213)(40 175 142 214)(41 176 143 215)(42 177 144 216)(43 105 132 76)(44 106 133 77)(45 107 134 78)(46 108 135 79)(47 109 136 80)(48 110 137 81)(49 111 138 82)(50 112 139 83)(51 99 140 84)(52 100 127 71)(53 101 128 72)(54 102 129 73)(55 103 130 74)(56 104 131 75)(57 158 64 165)(58 159 65 166)(59 160 66 167)(60 161 67 168)(61 162 68 155)(62 163 69 156)(63 164 70 157)(85 185 92 192)(86 186 93 193)(87 187 94 194)(88 188 95 195)(89 189 96 196)(90 190 97 183)(91 191 98 184)
(1 189 22 62)(2 190 23 63)(3 191 24 64)(4 192 25 65)(5 193 26 66)(6 194 27 67)(7 195 28 68)(8 196 15 69)(9 183 16 70)(10 184 17 57)(11 185 18 58)(12 186 19 59)(13 187 20 60)(14 188 21 61)(29 132 36 139)(30 133 37 140)(31 134 38 127)(32 135 39 128)(33 136 40 129)(34 137 41 130)(35 138 42 131)(43 152 50 145)(44 153 51 146)(45 154 52 147)(46 141 53 148)(47 142 54 149)(48 143 55 150)(49 144 56 151)(71 219 78 212)(72 220 79 213)(73 221 80 214)(74 222 81 215)(75 223 82 216)(76 224 83 217)(77 211 84 218)(85 117 166 201)(86 118 167 202)(87 119 168 203)(88 120 155 204)(89 121 156 205)(90 122 157 206)(91 123 158 207)(92 124 159 208)(93 125 160 209)(94 126 161 210)(95 113 162 197)(96 114 163 198)(97 115 164 199)(98 116 165 200)(99 179 106 172)(100 180 107 173)(101 181 108 174)(102 182 109 175)(103 169 110 176)(104 170 111 177)(105 171 112 178)
(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 46 22 53)(2 127 23 134)(3 44 24 51)(4 139 25 132)(5 56 26 49)(6 137 27 130)(7 54 28 47)(8 135 15 128)(9 52 16 45)(10 133 17 140)(11 50 18 43)(12 131 19 138)(13 48 20 55)(14 129 21 136)(29 159 36 92)(30 98 37 165)(31 157 38 90)(32 96 39 163)(33 155 40 88)(34 94 41 161)(35 167 42 86)(57 218 184 211)(58 171 185 178)(59 216 186 223)(60 169 187 176)(61 214 188 221)(62 181 189 174)(63 212 190 219)(64 179 191 172)(65 224 192 217)(66 177 193 170)(67 222 194 215)(68 175 195 182)(69 220 196 213)(70 173 183 180)(71 115 78 199)(72 205 79 121)(73 113 80 197)(74 203 81 119)(75 125 82 209)(76 201 83 117)(77 123 84 207)(85 145 166 152)(87 143 168 150)(89 141 156 148)(91 153 158 146)(93 151 160 144)(95 149 162 142)(97 147 164 154)(99 200 106 116)(100 122 107 206)(101 198 108 114)(102 120 109 204)(103 210 110 126)(104 118 111 202)(105 208 112 124)
G:=sub<Sym(224)| (1,205,8,198)(2,206,9,199)(3,207,10,200)(4,208,11,201)(5,209,12,202)(6,210,13,203)(7,197,14,204)(15,114,22,121)(16,115,23,122)(17,116,24,123)(18,117,25,124)(19,118,26,125)(20,119,27,126)(21,120,28,113)(29,178,145,217)(30,179,146,218)(31,180,147,219)(32,181,148,220)(33,182,149,221)(34,169,150,222)(35,170,151,223)(36,171,152,224)(37,172,153,211)(38,173,154,212)(39,174,141,213)(40,175,142,214)(41,176,143,215)(42,177,144,216)(43,105,132,76)(44,106,133,77)(45,107,134,78)(46,108,135,79)(47,109,136,80)(48,110,137,81)(49,111,138,82)(50,112,139,83)(51,99,140,84)(52,100,127,71)(53,101,128,72)(54,102,129,73)(55,103,130,74)(56,104,131,75)(57,158,64,165)(58,159,65,166)(59,160,66,167)(60,161,67,168)(61,162,68,155)(62,163,69,156)(63,164,70,157)(85,185,92,192)(86,186,93,193)(87,187,94,194)(88,188,95,195)(89,189,96,196)(90,190,97,183)(91,191,98,184), (1,189,22,62)(2,190,23,63)(3,191,24,64)(4,192,25,65)(5,193,26,66)(6,194,27,67)(7,195,28,68)(8,196,15,69)(9,183,16,70)(10,184,17,57)(11,185,18,58)(12,186,19,59)(13,187,20,60)(14,188,21,61)(29,132,36,139)(30,133,37,140)(31,134,38,127)(32,135,39,128)(33,136,40,129)(34,137,41,130)(35,138,42,131)(43,152,50,145)(44,153,51,146)(45,154,52,147)(46,141,53,148)(47,142,54,149)(48,143,55,150)(49,144,56,151)(71,219,78,212)(72,220,79,213)(73,221,80,214)(74,222,81,215)(75,223,82,216)(76,224,83,217)(77,211,84,218)(85,117,166,201)(86,118,167,202)(87,119,168,203)(88,120,155,204)(89,121,156,205)(90,122,157,206)(91,123,158,207)(92,124,159,208)(93,125,160,209)(94,126,161,210)(95,113,162,197)(96,114,163,198)(97,115,164,199)(98,116,165,200)(99,179,106,172)(100,180,107,173)(101,181,108,174)(102,182,109,175)(103,169,110,176)(104,170,111,177)(105,171,112,178), (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), (1,46,22,53)(2,127,23,134)(3,44,24,51)(4,139,25,132)(5,56,26,49)(6,137,27,130)(7,54,28,47)(8,135,15,128)(9,52,16,45)(10,133,17,140)(11,50,18,43)(12,131,19,138)(13,48,20,55)(14,129,21,136)(29,159,36,92)(30,98,37,165)(31,157,38,90)(32,96,39,163)(33,155,40,88)(34,94,41,161)(35,167,42,86)(57,218,184,211)(58,171,185,178)(59,216,186,223)(60,169,187,176)(61,214,188,221)(62,181,189,174)(63,212,190,219)(64,179,191,172)(65,224,192,217)(66,177,193,170)(67,222,194,215)(68,175,195,182)(69,220,196,213)(70,173,183,180)(71,115,78,199)(72,205,79,121)(73,113,80,197)(74,203,81,119)(75,125,82,209)(76,201,83,117)(77,123,84,207)(85,145,166,152)(87,143,168,150)(89,141,156,148)(91,153,158,146)(93,151,160,144)(95,149,162,142)(97,147,164,154)(99,200,106,116)(100,122,107,206)(101,198,108,114)(102,120,109,204)(103,210,110,126)(104,118,111,202)(105,208,112,124)>;
G:=Group( (1,205,8,198)(2,206,9,199)(3,207,10,200)(4,208,11,201)(5,209,12,202)(6,210,13,203)(7,197,14,204)(15,114,22,121)(16,115,23,122)(17,116,24,123)(18,117,25,124)(19,118,26,125)(20,119,27,126)(21,120,28,113)(29,178,145,217)(30,179,146,218)(31,180,147,219)(32,181,148,220)(33,182,149,221)(34,169,150,222)(35,170,151,223)(36,171,152,224)(37,172,153,211)(38,173,154,212)(39,174,141,213)(40,175,142,214)(41,176,143,215)(42,177,144,216)(43,105,132,76)(44,106,133,77)(45,107,134,78)(46,108,135,79)(47,109,136,80)(48,110,137,81)(49,111,138,82)(50,112,139,83)(51,99,140,84)(52,100,127,71)(53,101,128,72)(54,102,129,73)(55,103,130,74)(56,104,131,75)(57,158,64,165)(58,159,65,166)(59,160,66,167)(60,161,67,168)(61,162,68,155)(62,163,69,156)(63,164,70,157)(85,185,92,192)(86,186,93,193)(87,187,94,194)(88,188,95,195)(89,189,96,196)(90,190,97,183)(91,191,98,184), (1,189,22,62)(2,190,23,63)(3,191,24,64)(4,192,25,65)(5,193,26,66)(6,194,27,67)(7,195,28,68)(8,196,15,69)(9,183,16,70)(10,184,17,57)(11,185,18,58)(12,186,19,59)(13,187,20,60)(14,188,21,61)(29,132,36,139)(30,133,37,140)(31,134,38,127)(32,135,39,128)(33,136,40,129)(34,137,41,130)(35,138,42,131)(43,152,50,145)(44,153,51,146)(45,154,52,147)(46,141,53,148)(47,142,54,149)(48,143,55,150)(49,144,56,151)(71,219,78,212)(72,220,79,213)(73,221,80,214)(74,222,81,215)(75,223,82,216)(76,224,83,217)(77,211,84,218)(85,117,166,201)(86,118,167,202)(87,119,168,203)(88,120,155,204)(89,121,156,205)(90,122,157,206)(91,123,158,207)(92,124,159,208)(93,125,160,209)(94,126,161,210)(95,113,162,197)(96,114,163,198)(97,115,164,199)(98,116,165,200)(99,179,106,172)(100,180,107,173)(101,181,108,174)(102,182,109,175)(103,169,110,176)(104,170,111,177)(105,171,112,178), (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), (1,46,22,53)(2,127,23,134)(3,44,24,51)(4,139,25,132)(5,56,26,49)(6,137,27,130)(7,54,28,47)(8,135,15,128)(9,52,16,45)(10,133,17,140)(11,50,18,43)(12,131,19,138)(13,48,20,55)(14,129,21,136)(29,159,36,92)(30,98,37,165)(31,157,38,90)(32,96,39,163)(33,155,40,88)(34,94,41,161)(35,167,42,86)(57,218,184,211)(58,171,185,178)(59,216,186,223)(60,169,187,176)(61,214,188,221)(62,181,189,174)(63,212,190,219)(64,179,191,172)(65,224,192,217)(66,177,193,170)(67,222,194,215)(68,175,195,182)(69,220,196,213)(70,173,183,180)(71,115,78,199)(72,205,79,121)(73,113,80,197)(74,203,81,119)(75,125,82,209)(76,201,83,117)(77,123,84,207)(85,145,166,152)(87,143,168,150)(89,141,156,148)(91,153,158,146)(93,151,160,144)(95,149,162,142)(97,147,164,154)(99,200,106,116)(100,122,107,206)(101,198,108,114)(102,120,109,204)(103,210,110,126)(104,118,111,202)(105,208,112,124) );
G=PermutationGroup([[(1,205,8,198),(2,206,9,199),(3,207,10,200),(4,208,11,201),(5,209,12,202),(6,210,13,203),(7,197,14,204),(15,114,22,121),(16,115,23,122),(17,116,24,123),(18,117,25,124),(19,118,26,125),(20,119,27,126),(21,120,28,113),(29,178,145,217),(30,179,146,218),(31,180,147,219),(32,181,148,220),(33,182,149,221),(34,169,150,222),(35,170,151,223),(36,171,152,224),(37,172,153,211),(38,173,154,212),(39,174,141,213),(40,175,142,214),(41,176,143,215),(42,177,144,216),(43,105,132,76),(44,106,133,77),(45,107,134,78),(46,108,135,79),(47,109,136,80),(48,110,137,81),(49,111,138,82),(50,112,139,83),(51,99,140,84),(52,100,127,71),(53,101,128,72),(54,102,129,73),(55,103,130,74),(56,104,131,75),(57,158,64,165),(58,159,65,166),(59,160,66,167),(60,161,67,168),(61,162,68,155),(62,163,69,156),(63,164,70,157),(85,185,92,192),(86,186,93,193),(87,187,94,194),(88,188,95,195),(89,189,96,196),(90,190,97,183),(91,191,98,184)], [(1,189,22,62),(2,190,23,63),(3,191,24,64),(4,192,25,65),(5,193,26,66),(6,194,27,67),(7,195,28,68),(8,196,15,69),(9,183,16,70),(10,184,17,57),(11,185,18,58),(12,186,19,59),(13,187,20,60),(14,188,21,61),(29,132,36,139),(30,133,37,140),(31,134,38,127),(32,135,39,128),(33,136,40,129),(34,137,41,130),(35,138,42,131),(43,152,50,145),(44,153,51,146),(45,154,52,147),(46,141,53,148),(47,142,54,149),(48,143,55,150),(49,144,56,151),(71,219,78,212),(72,220,79,213),(73,221,80,214),(74,222,81,215),(75,223,82,216),(76,224,83,217),(77,211,84,218),(85,117,166,201),(86,118,167,202),(87,119,168,203),(88,120,155,204),(89,121,156,205),(90,122,157,206),(91,123,158,207),(92,124,159,208),(93,125,160,209),(94,126,161,210),(95,113,162,197),(96,114,163,198),(97,115,164,199),(98,116,165,200),(99,179,106,172),(100,180,107,173),(101,181,108,174),(102,182,109,175),(103,169,110,176),(104,170,111,177),(105,171,112,178)], [(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)], [(1,46,22,53),(2,127,23,134),(3,44,24,51),(4,139,25,132),(5,56,26,49),(6,137,27,130),(7,54,28,47),(8,135,15,128),(9,52,16,45),(10,133,17,140),(11,50,18,43),(12,131,19,138),(13,48,20,55),(14,129,21,136),(29,159,36,92),(30,98,37,165),(31,157,38,90),(32,96,39,163),(33,155,40,88),(34,94,41,161),(35,167,42,86),(57,218,184,211),(58,171,185,178),(59,216,186,223),(60,169,187,176),(61,214,188,221),(62,181,189,174),(63,212,190,219),(64,179,191,172),(65,224,192,217),(66,177,193,170),(67,222,194,215),(68,175,195,182),(69,220,196,213),(70,173,183,180),(71,115,78,199),(72,205,79,121),(73,113,80,197),(74,203,81,119),(75,125,82,209),(76,201,83,117),(77,123,84,207),(85,145,166,152),(87,143,168,150),(89,141,156,148),(91,153,158,146),(93,151,160,144),(95,149,162,142),(97,147,164,154),(99,200,106,116),(100,122,107,206),(101,198,108,114),(102,120,109,204),(103,210,110,126),(104,118,111,202),(105,208,112,124)]])
79 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 56 | 56 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 |
79 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | Q16 | D14 | D14 | C7⋊D4 | C7⋊D4 | C4○D28 | C8⋊C22 | C7⋊Q16 | D4.D14 |
| kernel | C4⋊C4.230D14 | C28.Q8 | C14.Q16 | C28.55D4 | C28.48D4 | C14×C4⋊C4 | C2×C28 | C22×C14 | C2×C4⋊C4 | C28 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C23 | C4 | C14 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 3 | 6 | 6 | 24 | 1 | 6 | 6 |
Matrix representation of C4⋊C4.230D14 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 1 | 15 |
| 0 | 0 | 30 | 112 |
| 15 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 49 | 93 |
| 0 | 0 | 41 | 64 |
| 28 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 0 | 109 | 0 | 0 |
| 85 | 0 | 0 | 0 |
| 0 | 0 | 81 | 41 |
| 0 | 0 | 88 | 32 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,1,30,0,0,15,112],[15,0,0,0,0,98,0,0,0,0,49,41,0,0,93,64],[28,0,0,0,0,4,0,0,0,0,112,0,0,0,0,112],[0,85,0,0,109,0,0,0,0,0,81,88,0,0,41,32] >;
C4⋊C4.230D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4._{230}D_{14} % in TeX
G:=Group("C4:C4.230D14"); // GroupNames label
G:=SmallGroup(448,504);
// by ID
G=gap.SmallGroup(448,504);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,254,268,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=b^2,b*a*b^-1=d*a*d^-1=a^-1,a*c=c*a,b*c=c*b,d*b*d^-1=a*b,d*c*d^-1=a^2*b^2*c^-1>;
// generators/relations