metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.30D14, C4⋊C8⋊15D7, (C4×D7).9Q8, C4.56(Q8×D7), (C4×D7).49D4, C28⋊C8⋊15C2, C4.209(D4×D7), Dic7⋊C8⋊24C2, D14⋊C4.14C4, D14.2(C4⋊C4), C28.368(C2×D4), (C2×C8).184D14, C28.114(C2×Q8), C14.13(C8○D4), Dic7⋊C4.14C4, Dic7.3(C4⋊C4), (C4×C28).65C22, C42⋊D7.1C2, (C2×C28).836C23, (C2×C56).215C22, C2.14(D28.C4), C7⋊1(C42.6C22), C2.15(D28.2C4), (C4×Dic7).185C22, (C7×C4⋊C8)⋊20C2, C14.9(C2×C4⋊C4), C2.10(D7×C4⋊C4), (D7×C2×C8).14C2, (C2×C4).36(C4×D7), (C2×C28).44(C2×C4), (C2×C8⋊D7).9C2, C22.114(C2×C4×D7), (C2×C7⋊C8).308C22, (C2×C4×D7).281C22, (C2×C14).91(C22×C4), (C2×Dic7).54(C2×C4), (C22×D7).39(C2×C4), (C2×C4).778(C22×D7), SmallGroup(448,373)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.30D14
G = < a,b,c,d | a4=b4=1, c14=b-1, d2=b, ab=ba, cac-1=a-1, dad-1=a-1b2, bc=cb, bd=db, dcd-1=b2c13 >
Subgroups: 452 in 114 conjugacy classes, 55 normal (47 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C2×C8, C2×C8, M4(2), C22×C4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C4⋊C8, C4⋊C8, C42⋊C2, C22×C8, C2×M4(2), C7⋊C8, C56, C4×D7, C2×Dic7, C2×C28, C22×D7, C42.6C22, C8×D7, C8⋊D7, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, D14⋊C4, C4×C28, C2×C56, C2×C4×D7, C28⋊C8, Dic7⋊C8, C7×C4⋊C8, C42⋊D7, D7×C2×C8, C2×C8⋊D7, C42.30D14
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, D14, C2×C4⋊C4, C8○D4, C4×D7, C22×D7, C42.6C22, C2×C4×D7, D4×D7, Q8×D7, D7×C4⋊C4, D28.2C4, D28.C4, C42.30D14
►On 224 points
Generators in S224
(1 66 177 139)(2 140 178 67)(3 68 179 141)(4 142 180 69)(5 70 181 143)(6 144 182 71)(7 72 183 145)(8 146 184 73)(9 74 185 147)(10 148 186 75)(11 76 187 149)(12 150 188 77)(13 78 189 151)(14 152 190 79)(15 80 191 153)(16 154 192 81)(17 82 193 155)(18 156 194 83)(19 84 195 157)(20 158 196 85)(21 86 197 159)(22 160 198 87)(23 88 199 161)(24 162 200 89)(25 90 201 163)(26 164 202 91)(27 92 203 165)(28 166 204 93)(29 94 205 167)(30 168 206 95)(31 96 207 113)(32 114 208 97)(33 98 209 115)(34 116 210 99)(35 100 211 117)(36 118 212 101)(37 102 213 119)(38 120 214 103)(39 104 215 121)(40 122 216 105)(41 106 217 123)(42 124 218 107)(43 108 219 125)(44 126 220 109)(45 110 221 127)(46 128 222 111)(47 112 223 129)(48 130 224 57)(49 58 169 131)(50 132 170 59)(51 60 171 133)(52 134 172 61)(53 62 173 135)(54 136 174 63)(55 64 175 137)(56 138 176 65)
(1 43 29 15)(2 44 30 16)(3 45 31 17)(4 46 32 18)(5 47 33 19)(6 48 34 20)(7 49 35 21)(8 50 36 22)(9 51 37 23)(10 52 38 24)(11 53 39 25)(12 54 40 26)(13 55 41 27)(14 56 42 28)(57 99 85 71)(58 100 86 72)(59 101 87 73)(60 102 88 74)(61 103 89 75)(62 104 90 76)(63 105 91 77)(64 106 92 78)(65 107 93 79)(66 108 94 80)(67 109 95 81)(68 110 96 82)(69 111 97 83)(70 112 98 84)(113 155 141 127)(114 156 142 128)(115 157 143 129)(116 158 144 130)(117 159 145 131)(118 160 146 132)(119 161 147 133)(120 162 148 134)(121 163 149 135)(122 164 150 136)(123 165 151 137)(124 166 152 138)(125 167 153 139)(126 168 154 140)(169 211 197 183)(170 212 198 184)(171 213 199 185)(172 214 200 186)(173 215 201 187)(174 216 202 188)(175 217 203 189)(176 218 204 190)(177 219 205 191)(178 220 206 192)(179 221 207 193)(180 222 208 194)(181 223 209 195)(182 224 210 196)
(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)
(1 218 43 204 29 190 15 176)(2 203 44 189 30 175 16 217)(3 188 45 174 31 216 17 202)(4 173 46 215 32 201 18 187)(5 214 47 200 33 186 19 172)(6 199 48 185 34 171 20 213)(7 184 49 170 35 212 21 198)(8 169 50 211 36 197 22 183)(9 210 51 196 37 182 23 224)(10 195 52 181 38 223 24 209)(11 180 53 222 39 208 25 194)(12 221 54 207 40 193 26 179)(13 206 55 192 41 178 27 220)(14 191 56 177 42 219 28 205)(57 119 99 161 85 147 71 133)(58 160 100 146 86 132 72 118)(59 145 101 131 87 117 73 159)(60 130 102 116 88 158 74 144)(61 115 103 157 89 143 75 129)(62 156 104 142 90 128 76 114)(63 141 105 127 91 113 77 155)(64 126 106 168 92 154 78 140)(65 167 107 153 93 139 79 125)(66 152 108 138 94 124 80 166)(67 137 109 123 95 165 81 151)(68 122 110 164 96 150 82 136)(69 163 111 149 97 135 83 121)(70 148 112 134 98 120 84 162)
G:=sub<Sym(224)| (1,66,177,139)(2,140,178,67)(3,68,179,141)(4,142,180,69)(5,70,181,143)(6,144,182,71)(7,72,183,145)(8,146,184,73)(9,74,185,147)(10,148,186,75)(11,76,187,149)(12,150,188,77)(13,78,189,151)(14,152,190,79)(15,80,191,153)(16,154,192,81)(17,82,193,155)(18,156,194,83)(19,84,195,157)(20,158,196,85)(21,86,197,159)(22,160,198,87)(23,88,199,161)(24,162,200,89)(25,90,201,163)(26,164,202,91)(27,92,203,165)(28,166,204,93)(29,94,205,167)(30,168,206,95)(31,96,207,113)(32,114,208,97)(33,98,209,115)(34,116,210,99)(35,100,211,117)(36,118,212,101)(37,102,213,119)(38,120,214,103)(39,104,215,121)(40,122,216,105)(41,106,217,123)(42,124,218,107)(43,108,219,125)(44,126,220,109)(45,110,221,127)(46,128,222,111)(47,112,223,129)(48,130,224,57)(49,58,169,131)(50,132,170,59)(51,60,171,133)(52,134,172,61)(53,62,173,135)(54,136,174,63)(55,64,175,137)(56,138,176,65), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,218,43,204,29,190,15,176)(2,203,44,189,30,175,16,217)(3,188,45,174,31,216,17,202)(4,173,46,215,32,201,18,187)(5,214,47,200,33,186,19,172)(6,199,48,185,34,171,20,213)(7,184,49,170,35,212,21,198)(8,169,50,211,36,197,22,183)(9,210,51,196,37,182,23,224)(10,195,52,181,38,223,24,209)(11,180,53,222,39,208,25,194)(12,221,54,207,40,193,26,179)(13,206,55,192,41,178,27,220)(14,191,56,177,42,219,28,205)(57,119,99,161,85,147,71,133)(58,160,100,146,86,132,72,118)(59,145,101,131,87,117,73,159)(60,130,102,116,88,158,74,144)(61,115,103,157,89,143,75,129)(62,156,104,142,90,128,76,114)(63,141,105,127,91,113,77,155)(64,126,106,168,92,154,78,140)(65,167,107,153,93,139,79,125)(66,152,108,138,94,124,80,166)(67,137,109,123,95,165,81,151)(68,122,110,164,96,150,82,136)(69,163,111,149,97,135,83,121)(70,148,112,134,98,120,84,162)>;
G:=Group( (1,66,177,139)(2,140,178,67)(3,68,179,141)(4,142,180,69)(5,70,181,143)(6,144,182,71)(7,72,183,145)(8,146,184,73)(9,74,185,147)(10,148,186,75)(11,76,187,149)(12,150,188,77)(13,78,189,151)(14,152,190,79)(15,80,191,153)(16,154,192,81)(17,82,193,155)(18,156,194,83)(19,84,195,157)(20,158,196,85)(21,86,197,159)(22,160,198,87)(23,88,199,161)(24,162,200,89)(25,90,201,163)(26,164,202,91)(27,92,203,165)(28,166,204,93)(29,94,205,167)(30,168,206,95)(31,96,207,113)(32,114,208,97)(33,98,209,115)(34,116,210,99)(35,100,211,117)(36,118,212,101)(37,102,213,119)(38,120,214,103)(39,104,215,121)(40,122,216,105)(41,106,217,123)(42,124,218,107)(43,108,219,125)(44,126,220,109)(45,110,221,127)(46,128,222,111)(47,112,223,129)(48,130,224,57)(49,58,169,131)(50,132,170,59)(51,60,171,133)(52,134,172,61)(53,62,173,135)(54,136,174,63)(55,64,175,137)(56,138,176,65), (1,43,29,15)(2,44,30,16)(3,45,31,17)(4,46,32,18)(5,47,33,19)(6,48,34,20)(7,49,35,21)(8,50,36,22)(9,51,37,23)(10,52,38,24)(11,53,39,25)(12,54,40,26)(13,55,41,27)(14,56,42,28)(57,99,85,71)(58,100,86,72)(59,101,87,73)(60,102,88,74)(61,103,89,75)(62,104,90,76)(63,105,91,77)(64,106,92,78)(65,107,93,79)(66,108,94,80)(67,109,95,81)(68,110,96,82)(69,111,97,83)(70,112,98,84)(113,155,141,127)(114,156,142,128)(115,157,143,129)(116,158,144,130)(117,159,145,131)(118,160,146,132)(119,161,147,133)(120,162,148,134)(121,163,149,135)(122,164,150,136)(123,165,151,137)(124,166,152,138)(125,167,153,139)(126,168,154,140)(169,211,197,183)(170,212,198,184)(171,213,199,185)(172,214,200,186)(173,215,201,187)(174,216,202,188)(175,217,203,189)(176,218,204,190)(177,219,205,191)(178,220,206,192)(179,221,207,193)(180,222,208,194)(181,223,209,195)(182,224,210,196), (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), (1,218,43,204,29,190,15,176)(2,203,44,189,30,175,16,217)(3,188,45,174,31,216,17,202)(4,173,46,215,32,201,18,187)(5,214,47,200,33,186,19,172)(6,199,48,185,34,171,20,213)(7,184,49,170,35,212,21,198)(8,169,50,211,36,197,22,183)(9,210,51,196,37,182,23,224)(10,195,52,181,38,223,24,209)(11,180,53,222,39,208,25,194)(12,221,54,207,40,193,26,179)(13,206,55,192,41,178,27,220)(14,191,56,177,42,219,28,205)(57,119,99,161,85,147,71,133)(58,160,100,146,86,132,72,118)(59,145,101,131,87,117,73,159)(60,130,102,116,88,158,74,144)(61,115,103,157,89,143,75,129)(62,156,104,142,90,128,76,114)(63,141,105,127,91,113,77,155)(64,126,106,168,92,154,78,140)(65,167,107,153,93,139,79,125)(66,152,108,138,94,124,80,166)(67,137,109,123,95,165,81,151)(68,122,110,164,96,150,82,136)(69,163,111,149,97,135,83,121)(70,148,112,134,98,120,84,162) );
G=PermutationGroup([[(1,66,177,139),(2,140,178,67),(3,68,179,141),(4,142,180,69),(5,70,181,143),(6,144,182,71),(7,72,183,145),(8,146,184,73),(9,74,185,147),(10,148,186,75),(11,76,187,149),(12,150,188,77),(13,78,189,151),(14,152,190,79),(15,80,191,153),(16,154,192,81),(17,82,193,155),(18,156,194,83),(19,84,195,157),(20,158,196,85),(21,86,197,159),(22,160,198,87),(23,88,199,161),(24,162,200,89),(25,90,201,163),(26,164,202,91),(27,92,203,165),(28,166,204,93),(29,94,205,167),(30,168,206,95),(31,96,207,113),(32,114,208,97),(33,98,209,115),(34,116,210,99),(35,100,211,117),(36,118,212,101),(37,102,213,119),(38,120,214,103),(39,104,215,121),(40,122,216,105),(41,106,217,123),(42,124,218,107),(43,108,219,125),(44,126,220,109),(45,110,221,127),(46,128,222,111),(47,112,223,129),(48,130,224,57),(49,58,169,131),(50,132,170,59),(51,60,171,133),(52,134,172,61),(53,62,173,135),(54,136,174,63),(55,64,175,137),(56,138,176,65)], [(1,43,29,15),(2,44,30,16),(3,45,31,17),(4,46,32,18),(5,47,33,19),(6,48,34,20),(7,49,35,21),(8,50,36,22),(9,51,37,23),(10,52,38,24),(11,53,39,25),(12,54,40,26),(13,55,41,27),(14,56,42,28),(57,99,85,71),(58,100,86,72),(59,101,87,73),(60,102,88,74),(61,103,89,75),(62,104,90,76),(63,105,91,77),(64,106,92,78),(65,107,93,79),(66,108,94,80),(67,109,95,81),(68,110,96,82),(69,111,97,83),(70,112,98,84),(113,155,141,127),(114,156,142,128),(115,157,143,129),(116,158,144,130),(117,159,145,131),(118,160,146,132),(119,161,147,133),(120,162,148,134),(121,163,149,135),(122,164,150,136),(123,165,151,137),(124,166,152,138),(125,167,153,139),(126,168,154,140),(169,211,197,183),(170,212,198,184),(171,213,199,185),(172,214,200,186),(173,215,201,187),(174,216,202,188),(175,217,203,189),(176,218,204,190),(177,219,205,191),(178,220,206,192),(179,221,207,193),(180,222,208,194),(181,223,209,195),(182,224,210,196)], [(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)], [(1,218,43,204,29,190,15,176),(2,203,44,189,30,175,16,217),(3,188,45,174,31,216,17,202),(4,173,46,215,32,201,18,187),(5,214,47,200,33,186,19,172),(6,199,48,185,34,171,20,213),(7,184,49,170,35,212,21,198),(8,169,50,211,36,197,22,183),(9,210,51,196,37,182,23,224),(10,195,52,181,38,223,24,209),(11,180,53,222,39,208,25,194),(12,221,54,207,40,193,26,179),(13,206,55,192,41,178,27,220),(14,191,56,177,42,219,28,205),(57,119,99,161,85,147,71,133),(58,160,100,146,86,132,72,118),(59,145,101,131,87,117,73,159),(60,130,102,116,88,158,74,144),(61,115,103,157,89,143,75,129),(62,156,104,142,90,128,76,114),(63,141,105,127,91,113,77,155),(64,126,106,168,92,154,78,140),(65,167,107,153,93,139,79,125),(66,152,108,138,94,124,80,166),(67,137,109,123,95,165,81,151),(68,122,110,164,96,150,82,136),(69,163,111,149,97,135,83,121),(70,148,112,134,98,120,84,162)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 8I | 8J | 8K | 8L | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28X | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 1 | 1 | 1 | 1 | 4 | 4 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | + | - | ||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | D4 | Q8 | D7 | D14 | D14 | C8○D4 | C4×D7 | D28.2C4 | D4×D7 | Q8×D7 | D28.C4 |
| kernel | C42.30D14 | C28⋊C8 | Dic7⋊C8 | C7×C4⋊C8 | C42⋊D7 | D7×C2×C8 | C2×C8⋊D7 | Dic7⋊C4 | D14⋊C4 | C4×D7 | C4×D7 | C4⋊C8 | C42 | C2×C8 | C14 | C2×C4 | C2 | C4 | C4 | C2 |
| # reps | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 4 | 4 | 2 | 2 | 3 | 3 | 6 | 8 | 12 | 24 | 3 | 3 | 6 |
Matrix representation of C42.30D14 ►in GL4(𝔽113) generated by
| 22 | 101 | 0 | 0 |
| 12 | 91 | 0 | 0 |
| 0 | 0 | 10 | 36 |
| 0 | 0 | 38 | 103 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 15 |
| 30 | 30 | 0 | 0 |
| 83 | 27 | 0 | 0 |
| 0 | 0 | 69 | 0 |
| 0 | 0 | 37 | 44 |
| 30 | 30 | 0 | 0 |
| 27 | 83 | 0 | 0 |
| 0 | 0 | 44 | 0 |
| 0 | 0 | 0 | 44 |
G:=sub<GL(4,GF(113))| [22,12,0,0,101,91,0,0,0,0,10,38,0,0,36,103],[15,0,0,0,0,15,0,0,0,0,15,0,0,0,0,15],[30,83,0,0,30,27,0,0,0,0,69,37,0,0,0,44],[30,27,0,0,30,83,0,0,0,0,44,0,0,0,0,44] >;
C42.30D14 in GAP, Magma, Sage, TeX
C_4^2._{30}D_{14} % in TeX
G:=Group("C4^2.30D14"); // GroupNames label
G:=SmallGroup(448,373);
// by ID
G=gap.SmallGroup(448,373);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,120,219,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^-1,d^2=b,a*b=b*a,c*a*c^-1=a^-1,d*a*d^-1=a^-1*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=b^2*c^13>;
// generators/relations