metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.88D14, (C2×C28)⋊4Q8, C28⋊Q8⋊46C2, (C2×C4)⋊7Dic14, C28.68(C2×Q8), C4⋊C4.266D14, (C4×Dic14)⋊6C2, (C4×C28).21C22, (C2×C14).61C24, C22⋊C4.89D14, C28.3Q8⋊45C2, C4.33(C2×Dic14), C14.10(C22×Q8), (C2×C28).140C23, Dic7.1(C4○D4), C42⋊C2.11D7, (C22×C4).362D14, C22.6(C2×Dic14), C22.94(C23×D7), C4⋊Dic7.360C22, C22⋊Dic14.5C2, C2.12(C22×Dic14), C23.150(C22×D7), C23.D7.91C22, Dic7⋊C4.105C22, (C22×C14).131C23, (C22×C28).222C22, C7⋊2(C23.37C23), (C4×Dic7).249C22, (C2×Dic7).193C23, (C2×Dic14).228C22, C23.21D14.22C2, (C22×Dic7).214C22, C2.8(D7×C4○D4), (C2×C14).12(C2×Q8), (C2×C4×Dic7).14C2, C14.130(C2×C4○D4), (C7×C4⋊C4).302C22, (C2×C4).574(C22×D7), (C7×C42⋊C2).12C2, (C7×C22⋊C4).98C22, SmallGroup(448,970)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.88D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, ab=ba, cac-1=ab2, dad-1=a-1, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 820 in 222 conjugacy classes, 115 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, C14, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Q8, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C2×C42, C42⋊C2, C42⋊C2, C4×Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.37C23, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×Dic7, C22×C28, C4×Dic14, C22⋊Dic14, C28⋊Q8, C28.3Q8, C2×C4×Dic7, C23.21D14, C7×C42⋊C2, C42.88D14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, Dic14, C22×D7, C23.37C23, C2×Dic14, C23×D7, C22×Dic14, D7×C4○D4, C42.88D14
►On 224 points
Generators in S224
(1 115 48 195)(2 123 49 189)(3 117 43 183)(4 125 44 191)(5 119 45 185)(6 113 46 193)(7 121 47 187)(8 133 15 169)(9 127 16 177)(10 135 17 171)(11 129 18 179)(12 137 19 173)(13 131 20 181)(14 139 21 175)(22 176 100 140)(23 170 101 134)(24 178 102 128)(25 172 103 136)(26 180 104 130)(27 174 105 138)(28 182 99 132)(29 209 90 216)(30 203 91 224)(31 197 85 218)(32 205 86 212)(33 199 87 220)(34 207 88 214)(35 201 89 222)(36 198 96 219)(37 206 97 213)(38 200 98 221)(39 208 92 215)(40 202 93 223)(41 210 94 217)(42 204 95 211)(50 194 78 114)(51 188 79 122)(52 196 80 116)(53 190 81 124)(54 184 82 118)(55 192 83 126)(56 186 84 120)(57 163 106 149)(58 157 107 143)(59 165 108 151)(60 159 109 145)(61 167 110 153)(62 161 111 147)(63 155 112 141)(64 156 71 142)(65 164 72 150)(66 158 73 144)(67 166 74 152)(68 160 75 146)(69 168 76 154)(70 162 77 148)
(1 38 79 34)(2 39 80 35)(3 40 81 29)(4 41 82 30)(5 42 83 31)(6 36 84 32)(7 37 78 33)(8 57 100 64)(9 58 101 65)(10 59 102 66)(11 60 103 67)(12 61 104 68)(13 62 105 69)(14 63 99 70)(15 106 22 71)(16 107 23 72)(17 108 24 73)(18 109 25 74)(19 110 26 75)(20 111 27 76)(21 112 28 77)(43 93 53 90)(44 94 54 91)(45 95 55 85)(46 96 56 86)(47 97 50 87)(48 98 51 88)(49 92 52 89)(113 198 120 205)(114 199 121 206)(115 200 122 207)(116 201 123 208)(117 202 124 209)(118 203 125 210)(119 204 126 197)(127 157 134 164)(128 158 135 165)(129 159 136 166)(130 160 137 167)(131 161 138 168)(132 162 139 155)(133 163 140 156)(141 182 148 175)(142 169 149 176)(143 170 150 177)(144 171 151 178)(145 172 152 179)(146 173 153 180)(147 174 154 181)(183 223 190 216)(184 224 191 217)(185 211 192 218)(186 212 193 219)(187 213 194 220)(188 214 195 221)(189 215 196 222)
(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)
(1 103 51 18)(2 102 52 17)(3 101 53 16)(4 100 54 15)(5 99 55 21)(6 105 56 20)(7 104 50 19)(8 44 22 82)(9 43 23 81)(10 49 24 80)(11 48 25 79)(12 47 26 78)(13 46 27 84)(14 45 28 83)(29 58 93 72)(30 57 94 71)(31 63 95 77)(32 62 96 76)(33 61 97 75)(34 60 98 74)(35 59 92 73)(36 69 86 111)(37 68 87 110)(38 67 88 109)(39 66 89 108)(40 65 90 107)(41 64 91 106)(42 70 85 112)(113 174 186 131)(114 173 187 130)(115 172 188 129)(116 171 189 128)(117 170 190 127)(118 169 191 140)(119 182 192 139)(120 181 193 138)(121 180 194 137)(122 179 195 136)(123 178 196 135)(124 177 183 134)(125 176 184 133)(126 175 185 132)(141 211 162 197)(142 224 163 210)(143 223 164 209)(144 222 165 208)(145 221 166 207)(146 220 167 206)(147 219 168 205)(148 218 155 204)(149 217 156 203)(150 216 157 202)(151 215 158 201)(152 214 159 200)(153 213 160 199)(154 212 161 198)
G:=sub<Sym(224)| (1,115,48,195)(2,123,49,189)(3,117,43,183)(4,125,44,191)(5,119,45,185)(6,113,46,193)(7,121,47,187)(8,133,15,169)(9,127,16,177)(10,135,17,171)(11,129,18,179)(12,137,19,173)(13,131,20,181)(14,139,21,175)(22,176,100,140)(23,170,101,134)(24,178,102,128)(25,172,103,136)(26,180,104,130)(27,174,105,138)(28,182,99,132)(29,209,90,216)(30,203,91,224)(31,197,85,218)(32,205,86,212)(33,199,87,220)(34,207,88,214)(35,201,89,222)(36,198,96,219)(37,206,97,213)(38,200,98,221)(39,208,92,215)(40,202,93,223)(41,210,94,217)(42,204,95,211)(50,194,78,114)(51,188,79,122)(52,196,80,116)(53,190,81,124)(54,184,82,118)(55,192,83,126)(56,186,84,120)(57,163,106,149)(58,157,107,143)(59,165,108,151)(60,159,109,145)(61,167,110,153)(62,161,111,147)(63,155,112,141)(64,156,71,142)(65,164,72,150)(66,158,73,144)(67,166,74,152)(68,160,75,146)(69,168,76,154)(70,162,77,148), (1,38,79,34)(2,39,80,35)(3,40,81,29)(4,41,82,30)(5,42,83,31)(6,36,84,32)(7,37,78,33)(8,57,100,64)(9,58,101,65)(10,59,102,66)(11,60,103,67)(12,61,104,68)(13,62,105,69)(14,63,99,70)(15,106,22,71)(16,107,23,72)(17,108,24,73)(18,109,25,74)(19,110,26,75)(20,111,27,76)(21,112,28,77)(43,93,53,90)(44,94,54,91)(45,95,55,85)(46,96,56,86)(47,97,50,87)(48,98,51,88)(49,92,52,89)(113,198,120,205)(114,199,121,206)(115,200,122,207)(116,201,123,208)(117,202,124,209)(118,203,125,210)(119,204,126,197)(127,157,134,164)(128,158,135,165)(129,159,136,166)(130,160,137,167)(131,161,138,168)(132,162,139,155)(133,163,140,156)(141,182,148,175)(142,169,149,176)(143,170,150,177)(144,171,151,178)(145,172,152,179)(146,173,153,180)(147,174,154,181)(183,223,190,216)(184,224,191,217)(185,211,192,218)(186,212,193,219)(187,213,194,220)(188,214,195,221)(189,215,196,222), (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), (1,103,51,18)(2,102,52,17)(3,101,53,16)(4,100,54,15)(5,99,55,21)(6,105,56,20)(7,104,50,19)(8,44,22,82)(9,43,23,81)(10,49,24,80)(11,48,25,79)(12,47,26,78)(13,46,27,84)(14,45,28,83)(29,58,93,72)(30,57,94,71)(31,63,95,77)(32,62,96,76)(33,61,97,75)(34,60,98,74)(35,59,92,73)(36,69,86,111)(37,68,87,110)(38,67,88,109)(39,66,89,108)(40,65,90,107)(41,64,91,106)(42,70,85,112)(113,174,186,131)(114,173,187,130)(115,172,188,129)(116,171,189,128)(117,170,190,127)(118,169,191,140)(119,182,192,139)(120,181,193,138)(121,180,194,137)(122,179,195,136)(123,178,196,135)(124,177,183,134)(125,176,184,133)(126,175,185,132)(141,211,162,197)(142,224,163,210)(143,223,164,209)(144,222,165,208)(145,221,166,207)(146,220,167,206)(147,219,168,205)(148,218,155,204)(149,217,156,203)(150,216,157,202)(151,215,158,201)(152,214,159,200)(153,213,160,199)(154,212,161,198)>;
G:=Group( (1,115,48,195)(2,123,49,189)(3,117,43,183)(4,125,44,191)(5,119,45,185)(6,113,46,193)(7,121,47,187)(8,133,15,169)(9,127,16,177)(10,135,17,171)(11,129,18,179)(12,137,19,173)(13,131,20,181)(14,139,21,175)(22,176,100,140)(23,170,101,134)(24,178,102,128)(25,172,103,136)(26,180,104,130)(27,174,105,138)(28,182,99,132)(29,209,90,216)(30,203,91,224)(31,197,85,218)(32,205,86,212)(33,199,87,220)(34,207,88,214)(35,201,89,222)(36,198,96,219)(37,206,97,213)(38,200,98,221)(39,208,92,215)(40,202,93,223)(41,210,94,217)(42,204,95,211)(50,194,78,114)(51,188,79,122)(52,196,80,116)(53,190,81,124)(54,184,82,118)(55,192,83,126)(56,186,84,120)(57,163,106,149)(58,157,107,143)(59,165,108,151)(60,159,109,145)(61,167,110,153)(62,161,111,147)(63,155,112,141)(64,156,71,142)(65,164,72,150)(66,158,73,144)(67,166,74,152)(68,160,75,146)(69,168,76,154)(70,162,77,148), (1,38,79,34)(2,39,80,35)(3,40,81,29)(4,41,82,30)(5,42,83,31)(6,36,84,32)(7,37,78,33)(8,57,100,64)(9,58,101,65)(10,59,102,66)(11,60,103,67)(12,61,104,68)(13,62,105,69)(14,63,99,70)(15,106,22,71)(16,107,23,72)(17,108,24,73)(18,109,25,74)(19,110,26,75)(20,111,27,76)(21,112,28,77)(43,93,53,90)(44,94,54,91)(45,95,55,85)(46,96,56,86)(47,97,50,87)(48,98,51,88)(49,92,52,89)(113,198,120,205)(114,199,121,206)(115,200,122,207)(116,201,123,208)(117,202,124,209)(118,203,125,210)(119,204,126,197)(127,157,134,164)(128,158,135,165)(129,159,136,166)(130,160,137,167)(131,161,138,168)(132,162,139,155)(133,163,140,156)(141,182,148,175)(142,169,149,176)(143,170,150,177)(144,171,151,178)(145,172,152,179)(146,173,153,180)(147,174,154,181)(183,223,190,216)(184,224,191,217)(185,211,192,218)(186,212,193,219)(187,213,194,220)(188,214,195,221)(189,215,196,222), (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), (1,103,51,18)(2,102,52,17)(3,101,53,16)(4,100,54,15)(5,99,55,21)(6,105,56,20)(7,104,50,19)(8,44,22,82)(9,43,23,81)(10,49,24,80)(11,48,25,79)(12,47,26,78)(13,46,27,84)(14,45,28,83)(29,58,93,72)(30,57,94,71)(31,63,95,77)(32,62,96,76)(33,61,97,75)(34,60,98,74)(35,59,92,73)(36,69,86,111)(37,68,87,110)(38,67,88,109)(39,66,89,108)(40,65,90,107)(41,64,91,106)(42,70,85,112)(113,174,186,131)(114,173,187,130)(115,172,188,129)(116,171,189,128)(117,170,190,127)(118,169,191,140)(119,182,192,139)(120,181,193,138)(121,180,194,137)(122,179,195,136)(123,178,196,135)(124,177,183,134)(125,176,184,133)(126,175,185,132)(141,211,162,197)(142,224,163,210)(143,223,164,209)(144,222,165,208)(145,221,166,207)(146,220,167,206)(147,219,168,205)(148,218,155,204)(149,217,156,203)(150,216,157,202)(151,215,158,201)(152,214,159,200)(153,213,160,199)(154,212,161,198) );
G=PermutationGroup([[(1,115,48,195),(2,123,49,189),(3,117,43,183),(4,125,44,191),(5,119,45,185),(6,113,46,193),(7,121,47,187),(8,133,15,169),(9,127,16,177),(10,135,17,171),(11,129,18,179),(12,137,19,173),(13,131,20,181),(14,139,21,175),(22,176,100,140),(23,170,101,134),(24,178,102,128),(25,172,103,136),(26,180,104,130),(27,174,105,138),(28,182,99,132),(29,209,90,216),(30,203,91,224),(31,197,85,218),(32,205,86,212),(33,199,87,220),(34,207,88,214),(35,201,89,222),(36,198,96,219),(37,206,97,213),(38,200,98,221),(39,208,92,215),(40,202,93,223),(41,210,94,217),(42,204,95,211),(50,194,78,114),(51,188,79,122),(52,196,80,116),(53,190,81,124),(54,184,82,118),(55,192,83,126),(56,186,84,120),(57,163,106,149),(58,157,107,143),(59,165,108,151),(60,159,109,145),(61,167,110,153),(62,161,111,147),(63,155,112,141),(64,156,71,142),(65,164,72,150),(66,158,73,144),(67,166,74,152),(68,160,75,146),(69,168,76,154),(70,162,77,148)], [(1,38,79,34),(2,39,80,35),(3,40,81,29),(4,41,82,30),(5,42,83,31),(6,36,84,32),(7,37,78,33),(8,57,100,64),(9,58,101,65),(10,59,102,66),(11,60,103,67),(12,61,104,68),(13,62,105,69),(14,63,99,70),(15,106,22,71),(16,107,23,72),(17,108,24,73),(18,109,25,74),(19,110,26,75),(20,111,27,76),(21,112,28,77),(43,93,53,90),(44,94,54,91),(45,95,55,85),(46,96,56,86),(47,97,50,87),(48,98,51,88),(49,92,52,89),(113,198,120,205),(114,199,121,206),(115,200,122,207),(116,201,123,208),(117,202,124,209),(118,203,125,210),(119,204,126,197),(127,157,134,164),(128,158,135,165),(129,159,136,166),(130,160,137,167),(131,161,138,168),(132,162,139,155),(133,163,140,156),(141,182,148,175),(142,169,149,176),(143,170,150,177),(144,171,151,178),(145,172,152,179),(146,173,153,180),(147,174,154,181),(183,223,190,216),(184,224,191,217),(185,211,192,218),(186,212,193,219),(187,213,194,220),(188,214,195,221),(189,215,196,222)], [(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)], [(1,103,51,18),(2,102,52,17),(3,101,53,16),(4,100,54,15),(5,99,55,21),(6,105,56,20),(7,104,50,19),(8,44,22,82),(9,43,23,81),(10,49,24,80),(11,48,25,79),(12,47,26,78),(13,46,27,84),(14,45,28,83),(29,58,93,72),(30,57,94,71),(31,63,95,77),(32,62,96,76),(33,61,97,75),(34,60,98,74),(35,59,92,73),(36,69,86,111),(37,68,87,110),(38,67,88,109),(39,66,89,108),(40,65,90,107),(41,64,91,106),(42,70,85,112),(113,174,186,131),(114,173,187,130),(115,172,188,129),(116,171,189,128),(117,170,190,127),(118,169,191,140),(119,182,192,139),(120,181,193,138),(121,180,194,137),(122,179,195,136),(123,178,196,135),(124,177,183,134),(125,176,184,133),(126,175,185,132),(141,211,162,197),(142,224,163,210),(143,223,164,209),(144,222,165,208),(145,221,166,207),(146,220,167,206),(147,219,168,205),(148,218,155,204),(149,217,156,203),(150,216,157,202),(151,215,158,201),(152,214,159,200),(153,213,160,199),(154,212,161,198)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4R | 4S | 4T | 4U | 4V | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 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 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | D14 | D14 | Dic14 | D7×C4○D4 |
| kernel | C42.88D14 | C4×Dic14 | C22⋊Dic14 | C28⋊Q8 | C28.3Q8 | C2×C4×Dic7 | C23.21D14 | C7×C42⋊C2 | C2×C28 | C42⋊C2 | Dic7 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C2 |
| # reps | 1 | 4 | 4 | 2 | 2 | 1 | 1 | 1 | 4 | 3 | 8 | 6 | 6 | 6 | 3 | 24 | 12 |
Matrix representation of C42.88D14 ►in GL4(𝔽29) generated by
| 15 | 7 | 0 | 0 |
| 26 | 14 | 0 | 0 |
| 0 | 0 | 17 | 0 |
| 0 | 0 | 10 | 12 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 |
| 4 | 28 | 0 | 0 |
| 0 | 0 | 20 | 0 |
| 0 | 0 | 8 | 16 |
| 17 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 |
| 0 | 0 | 3 | 13 |
| 0 | 0 | 26 | 26 |
G:=sub<GL(4,GF(29))| [15,26,0,0,7,14,0,0,0,0,17,10,0,0,0,12],[17,0,0,0,0,17,0,0,0,0,28,0,0,0,0,28],[1,4,0,0,0,28,0,0,0,0,20,8,0,0,0,16],[17,0,0,0,0,17,0,0,0,0,3,26,0,0,13,26] >;
C42.88D14 in GAP, Magma, Sage, TeX
C_4^2._{88}D_{14} % in TeX
G:=Group("C4^2.88D14"); // GroupNames label
G:=SmallGroup(448,970);
// by ID
G=gap.SmallGroup(448,970);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,184,675,570,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=a*b^2,d*a*d^-1=a^-1,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations