metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.145D14, C14.742+ (1+4), C14.932- (1+4), C4.4D4⋊17D7, (C2×Q8).84D14, D14⋊D4⋊43C2, D14⋊3Q8⋊34C2, (C2×D4).113D14, C4.D28⋊31C2, C22⋊C4.38D14, C28.6Q8⋊29C2, Dic7⋊D4⋊35C2, D14.D4⋊47C2, (C2×C14).228C24, (C2×C28).633C23, (C4×C28).222C22, D14⋊C4.73C22, (C2×D28).35C22, C4⋊Dic7.52C22, C2.78(D4⋊6D14), C2.54(D4⋊8D14), C23.50(C22×D7), C22⋊Dic14⋊43C2, (D4×C14).213C22, C22.D28⋊28C2, Dic7⋊C4.84C22, (C22×C14).58C23, (Q8×C14).131C22, C22.249(C23×D7), C23.D7.60C22, C7⋊4(C22.56C24), (C2×Dic14).39C22, (C2×Dic7).118C23, (C22×D7).100C23, C2.54(D4.10D14), (C22×Dic7).147C22, (C7×C4.4D4)⋊20C2, (C2×C4×D7).123C22, (C2×C4).201(C22×D7), (C2×C7⋊D4).66C22, (C7×C22⋊C4).69C22, SmallGroup(448,1137)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1100 in 220 conjugacy classes, 91 normal (31 characteristic)
C1, C2 [×3], C2 [×4], C4 [×11], C22, C22 [×12], C7, C2×C4 [×3], C2×C4 [×2], C2×C4 [×10], D4 [×6], Q8 [×2], C23 [×2], C23 [×2], D7 [×2], C14 [×3], C14 [×2], C42, C22⋊C4 [×4], C22⋊C4 [×8], C4⋊C4 [×10], C22×C4 [×4], C2×D4, C2×D4 [×5], C2×Q8, C2×Q8, Dic7 [×6], C28 [×5], D14 [×6], C2×C14, C2×C14 [×6], C4⋊D4 [×4], C22⋊Q8 [×4], C22.D4 [×4], C4.4D4, C4.4D4, C42.C2, Dic14, C4×D7 [×2], D28, C2×Dic7 [×6], C2×Dic7 [×2], C7⋊D4 [×4], C2×C28 [×3], C2×C28 [×2], C7×D4, C7×Q8, C22×D7 [×2], C22×C14 [×2], C22.56C24, Dic7⋊C4 [×6], C4⋊Dic7 [×2], C4⋊Dic7 [×2], D14⋊C4 [×6], C23.D7 [×2], C4×C28, C7×C22⋊C4 [×4], C2×Dic14, C2×C4×D7 [×2], C2×D28, C22×Dic7 [×2], C2×C7⋊D4 [×4], D4×C14, Q8×C14, C28.6Q8, C4.D28, C22⋊Dic14 [×2], D14.D4 [×2], D14⋊D4 [×2], C22.D28 [×2], Dic7⋊D4 [×2], D14⋊3Q8 [×2], C7×C4.4D4, C42.145D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C24, D14 [×7], 2+ (1+4) [×2], 2- (1+4), C22×D7 [×7], C22.56C24, C23×D7, D4⋊6D14, D4⋊8D14, D4.10D14, C42.145D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=b2, ab=ba, cac-1=a-1b2, dad-1=a-1, cbc-1=b-1, dbd-1=a2b-1, dcd-1=c13 >
►On 224 points
Generators in S224
(1 77 115 171)(2 186 116 64)(3 79 117 173)(4 188 118 66)(5 81 119 175)(6 190 120 68)(7 83 121 177)(8 192 122 70)(9 57 123 179)(10 194 124 72)(11 59 125 181)(12 196 126 74)(13 61 127 183)(14 170 128 76)(15 63 129 185)(16 172 130 78)(17 65 131 187)(18 174 132 80)(19 67 133 189)(20 176 134 82)(21 69 135 191)(22 178 136 84)(23 71 137 193)(24 180 138 58)(25 73 139 195)(26 182 140 60)(27 75 113 169)(28 184 114 62)(29 158 215 102)(30 89 216 145)(31 160 217 104)(32 91 218 147)(33 162 219 106)(34 93 220 149)(35 164 221 108)(36 95 222 151)(37 166 223 110)(38 97 224 153)(39 168 197 112)(40 99 198 155)(41 142 199 86)(42 101 200 157)(43 144 201 88)(44 103 202 159)(45 146 203 90)(46 105 204 161)(47 148 205 92)(48 107 206 163)(49 150 207 94)(50 109 208 165)(51 152 209 96)(52 111 210 167)(53 154 211 98)(54 85 212 141)(55 156 213 100)(56 87 214 143)
(1 178 15 192)(2 193 16 179)(3 180 17 194)(4 195 18 181)(5 182 19 196)(6 169 20 183)(7 184 21 170)(8 171 22 185)(9 186 23 172)(10 173 24 187)(11 188 25 174)(12 175 26 189)(13 190 27 176)(14 177 28 191)(29 95 43 109)(30 110 44 96)(31 97 45 111)(32 112 46 98)(33 99 47 85)(34 86 48 100)(35 101 49 87)(36 88 50 102)(37 103 51 89)(38 90 52 104)(39 105 53 91)(40 92 54 106)(41 107 55 93)(42 94 56 108)(57 116 71 130)(58 131 72 117)(59 118 73 132)(60 133 74 119)(61 120 75 134)(62 135 76 121)(63 122 77 136)(64 137 78 123)(65 124 79 138)(66 139 80 125)(67 126 81 140)(68 113 82 127)(69 128 83 114)(70 115 84 129)(141 219 155 205)(142 206 156 220)(143 221 157 207)(144 208 158 222)(145 223 159 209)(146 210 160 224)(147 197 161 211)(148 212 162 198)(149 199 163 213)(150 214 164 200)(151 201 165 215)(152 216 166 202)(153 203 167 217)(154 218 168 204)
(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)
(1 201 15 215)(2 214 16 200)(3 199 17 213)(4 212 18 198)(5 197 19 211)(6 210 20 224)(7 223 21 209)(8 208 22 222)(9 221 23 207)(10 206 24 220)(11 219 25 205)(12 204 26 218)(13 217 27 203)(14 202 28 216)(29 115 43 129)(30 128 44 114)(31 113 45 127)(32 126 46 140)(33 139 47 125)(34 124 48 138)(35 137 49 123)(36 122 50 136)(37 135 51 121)(38 120 52 134)(39 133 53 119)(40 118 54 132)(41 131 55 117)(42 116 56 130)(57 164 71 150)(58 149 72 163)(59 162 73 148)(60 147 74 161)(61 160 75 146)(62 145 76 159)(63 158 77 144)(64 143 78 157)(65 156 79 142)(66 141 80 155)(67 154 81 168)(68 167 82 153)(69 152 83 166)(70 165 84 151)(85 174 99 188)(86 187 100 173)(87 172 101 186)(88 185 102 171)(89 170 103 184)(90 183 104 169)(91 196 105 182)(92 181 106 195)(93 194 107 180)(94 179 108 193)(95 192 109 178)(96 177 110 191)(97 190 111 176)(98 175 112 189)
G:=sub<Sym(224)| (1,77,115,171)(2,186,116,64)(3,79,117,173)(4,188,118,66)(5,81,119,175)(6,190,120,68)(7,83,121,177)(8,192,122,70)(9,57,123,179)(10,194,124,72)(11,59,125,181)(12,196,126,74)(13,61,127,183)(14,170,128,76)(15,63,129,185)(16,172,130,78)(17,65,131,187)(18,174,132,80)(19,67,133,189)(20,176,134,82)(21,69,135,191)(22,178,136,84)(23,71,137,193)(24,180,138,58)(25,73,139,195)(26,182,140,60)(27,75,113,169)(28,184,114,62)(29,158,215,102)(30,89,216,145)(31,160,217,104)(32,91,218,147)(33,162,219,106)(34,93,220,149)(35,164,221,108)(36,95,222,151)(37,166,223,110)(38,97,224,153)(39,168,197,112)(40,99,198,155)(41,142,199,86)(42,101,200,157)(43,144,201,88)(44,103,202,159)(45,146,203,90)(46,105,204,161)(47,148,205,92)(48,107,206,163)(49,150,207,94)(50,109,208,165)(51,152,209,96)(52,111,210,167)(53,154,211,98)(54,85,212,141)(55,156,213,100)(56,87,214,143), (1,178,15,192)(2,193,16,179)(3,180,17,194)(4,195,18,181)(5,182,19,196)(6,169,20,183)(7,184,21,170)(8,171,22,185)(9,186,23,172)(10,173,24,187)(11,188,25,174)(12,175,26,189)(13,190,27,176)(14,177,28,191)(29,95,43,109)(30,110,44,96)(31,97,45,111)(32,112,46,98)(33,99,47,85)(34,86,48,100)(35,101,49,87)(36,88,50,102)(37,103,51,89)(38,90,52,104)(39,105,53,91)(40,92,54,106)(41,107,55,93)(42,94,56,108)(57,116,71,130)(58,131,72,117)(59,118,73,132)(60,133,74,119)(61,120,75,134)(62,135,76,121)(63,122,77,136)(64,137,78,123)(65,124,79,138)(66,139,80,125)(67,126,81,140)(68,113,82,127)(69,128,83,114)(70,115,84,129)(141,219,155,205)(142,206,156,220)(143,221,157,207)(144,208,158,222)(145,223,159,209)(146,210,160,224)(147,197,161,211)(148,212,162,198)(149,199,163,213)(150,214,164,200)(151,201,165,215)(152,216,166,202)(153,203,167,217)(154,218,168,204), (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), (1,201,15,215)(2,214,16,200)(3,199,17,213)(4,212,18,198)(5,197,19,211)(6,210,20,224)(7,223,21,209)(8,208,22,222)(9,221,23,207)(10,206,24,220)(11,219,25,205)(12,204,26,218)(13,217,27,203)(14,202,28,216)(29,115,43,129)(30,128,44,114)(31,113,45,127)(32,126,46,140)(33,139,47,125)(34,124,48,138)(35,137,49,123)(36,122,50,136)(37,135,51,121)(38,120,52,134)(39,133,53,119)(40,118,54,132)(41,131,55,117)(42,116,56,130)(57,164,71,150)(58,149,72,163)(59,162,73,148)(60,147,74,161)(61,160,75,146)(62,145,76,159)(63,158,77,144)(64,143,78,157)(65,156,79,142)(66,141,80,155)(67,154,81,168)(68,167,82,153)(69,152,83,166)(70,165,84,151)(85,174,99,188)(86,187,100,173)(87,172,101,186)(88,185,102,171)(89,170,103,184)(90,183,104,169)(91,196,105,182)(92,181,106,195)(93,194,107,180)(94,179,108,193)(95,192,109,178)(96,177,110,191)(97,190,111,176)(98,175,112,189)>;
G:=Group( (1,77,115,171)(2,186,116,64)(3,79,117,173)(4,188,118,66)(5,81,119,175)(6,190,120,68)(7,83,121,177)(8,192,122,70)(9,57,123,179)(10,194,124,72)(11,59,125,181)(12,196,126,74)(13,61,127,183)(14,170,128,76)(15,63,129,185)(16,172,130,78)(17,65,131,187)(18,174,132,80)(19,67,133,189)(20,176,134,82)(21,69,135,191)(22,178,136,84)(23,71,137,193)(24,180,138,58)(25,73,139,195)(26,182,140,60)(27,75,113,169)(28,184,114,62)(29,158,215,102)(30,89,216,145)(31,160,217,104)(32,91,218,147)(33,162,219,106)(34,93,220,149)(35,164,221,108)(36,95,222,151)(37,166,223,110)(38,97,224,153)(39,168,197,112)(40,99,198,155)(41,142,199,86)(42,101,200,157)(43,144,201,88)(44,103,202,159)(45,146,203,90)(46,105,204,161)(47,148,205,92)(48,107,206,163)(49,150,207,94)(50,109,208,165)(51,152,209,96)(52,111,210,167)(53,154,211,98)(54,85,212,141)(55,156,213,100)(56,87,214,143), (1,178,15,192)(2,193,16,179)(3,180,17,194)(4,195,18,181)(5,182,19,196)(6,169,20,183)(7,184,21,170)(8,171,22,185)(9,186,23,172)(10,173,24,187)(11,188,25,174)(12,175,26,189)(13,190,27,176)(14,177,28,191)(29,95,43,109)(30,110,44,96)(31,97,45,111)(32,112,46,98)(33,99,47,85)(34,86,48,100)(35,101,49,87)(36,88,50,102)(37,103,51,89)(38,90,52,104)(39,105,53,91)(40,92,54,106)(41,107,55,93)(42,94,56,108)(57,116,71,130)(58,131,72,117)(59,118,73,132)(60,133,74,119)(61,120,75,134)(62,135,76,121)(63,122,77,136)(64,137,78,123)(65,124,79,138)(66,139,80,125)(67,126,81,140)(68,113,82,127)(69,128,83,114)(70,115,84,129)(141,219,155,205)(142,206,156,220)(143,221,157,207)(144,208,158,222)(145,223,159,209)(146,210,160,224)(147,197,161,211)(148,212,162,198)(149,199,163,213)(150,214,164,200)(151,201,165,215)(152,216,166,202)(153,203,167,217)(154,218,168,204), (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), (1,201,15,215)(2,214,16,200)(3,199,17,213)(4,212,18,198)(5,197,19,211)(6,210,20,224)(7,223,21,209)(8,208,22,222)(9,221,23,207)(10,206,24,220)(11,219,25,205)(12,204,26,218)(13,217,27,203)(14,202,28,216)(29,115,43,129)(30,128,44,114)(31,113,45,127)(32,126,46,140)(33,139,47,125)(34,124,48,138)(35,137,49,123)(36,122,50,136)(37,135,51,121)(38,120,52,134)(39,133,53,119)(40,118,54,132)(41,131,55,117)(42,116,56,130)(57,164,71,150)(58,149,72,163)(59,162,73,148)(60,147,74,161)(61,160,75,146)(62,145,76,159)(63,158,77,144)(64,143,78,157)(65,156,79,142)(66,141,80,155)(67,154,81,168)(68,167,82,153)(69,152,83,166)(70,165,84,151)(85,174,99,188)(86,187,100,173)(87,172,101,186)(88,185,102,171)(89,170,103,184)(90,183,104,169)(91,196,105,182)(92,181,106,195)(93,194,107,180)(94,179,108,193)(95,192,109,178)(96,177,110,191)(97,190,111,176)(98,175,112,189) );
G=PermutationGroup([(1,77,115,171),(2,186,116,64),(3,79,117,173),(4,188,118,66),(5,81,119,175),(6,190,120,68),(7,83,121,177),(8,192,122,70),(9,57,123,179),(10,194,124,72),(11,59,125,181),(12,196,126,74),(13,61,127,183),(14,170,128,76),(15,63,129,185),(16,172,130,78),(17,65,131,187),(18,174,132,80),(19,67,133,189),(20,176,134,82),(21,69,135,191),(22,178,136,84),(23,71,137,193),(24,180,138,58),(25,73,139,195),(26,182,140,60),(27,75,113,169),(28,184,114,62),(29,158,215,102),(30,89,216,145),(31,160,217,104),(32,91,218,147),(33,162,219,106),(34,93,220,149),(35,164,221,108),(36,95,222,151),(37,166,223,110),(38,97,224,153),(39,168,197,112),(40,99,198,155),(41,142,199,86),(42,101,200,157),(43,144,201,88),(44,103,202,159),(45,146,203,90),(46,105,204,161),(47,148,205,92),(48,107,206,163),(49,150,207,94),(50,109,208,165),(51,152,209,96),(52,111,210,167),(53,154,211,98),(54,85,212,141),(55,156,213,100),(56,87,214,143)], [(1,178,15,192),(2,193,16,179),(3,180,17,194),(4,195,18,181),(5,182,19,196),(6,169,20,183),(7,184,21,170),(8,171,22,185),(9,186,23,172),(10,173,24,187),(11,188,25,174),(12,175,26,189),(13,190,27,176),(14,177,28,191),(29,95,43,109),(30,110,44,96),(31,97,45,111),(32,112,46,98),(33,99,47,85),(34,86,48,100),(35,101,49,87),(36,88,50,102),(37,103,51,89),(38,90,52,104),(39,105,53,91),(40,92,54,106),(41,107,55,93),(42,94,56,108),(57,116,71,130),(58,131,72,117),(59,118,73,132),(60,133,74,119),(61,120,75,134),(62,135,76,121),(63,122,77,136),(64,137,78,123),(65,124,79,138),(66,139,80,125),(67,126,81,140),(68,113,82,127),(69,128,83,114),(70,115,84,129),(141,219,155,205),(142,206,156,220),(143,221,157,207),(144,208,158,222),(145,223,159,209),(146,210,160,224),(147,197,161,211),(148,212,162,198),(149,199,163,213),(150,214,164,200),(151,201,165,215),(152,216,166,202),(153,203,167,217),(154,218,168,204)], [(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)], [(1,201,15,215),(2,214,16,200),(3,199,17,213),(4,212,18,198),(5,197,19,211),(6,210,20,224),(7,223,21,209),(8,208,22,222),(9,221,23,207),(10,206,24,220),(11,219,25,205),(12,204,26,218),(13,217,27,203),(14,202,28,216),(29,115,43,129),(30,128,44,114),(31,113,45,127),(32,126,46,140),(33,139,47,125),(34,124,48,138),(35,137,49,123),(36,122,50,136),(37,135,51,121),(38,120,52,134),(39,133,53,119),(40,118,54,132),(41,131,55,117),(42,116,56,130),(57,164,71,150),(58,149,72,163),(59,162,73,148),(60,147,74,161),(61,160,75,146),(62,145,76,159),(63,158,77,144),(64,143,78,157),(65,156,79,142),(66,141,80,155),(67,154,81,168),(68,167,82,153),(69,152,83,166),(70,165,84,151),(85,174,99,188),(86,187,100,173),(87,172,101,186),(88,185,102,171),(89,170,103,184),(90,183,104,169),(91,196,105,182),(92,181,106,195),(93,194,107,180),(94,179,108,193),(95,192,109,178),(96,177,110,191),(97,190,111,176),(98,175,112,189)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 16 | 24 | 10 | 6 | 0 | 0 | 0 | 0 |
| 5 | 13 | 21 | 20 | 0 | 0 | 0 | 0 |
| 17 | 21 | 27 | 5 | 0 | 0 | 0 | 0 |
| 1 | 23 | 28 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 | 23 | 10 |
| 0 | 0 | 0 | 0 | 14 | 9 | 27 | 7 |
| 0 | 0 | 0 | 0 | 27 | 7 | 25 | 14 |
| 0 | 0 | 0 | 0 | 16 | 10 | 1 | 4 |
| 1 | 0 | 3 | 4 | 0 | 0 | 0 | 0 |
| 0 | 1 | 25 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 28 | 0 | 0 | 0 | 0 | 0 |
| 14 | 25 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 | 15 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 25 |
| 26 | 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 26 | 22 | 0 | 0 | 0 | 0 | 0 | 0 |
| 13 | 11 | 12 | 26 | 0 | 0 | 0 | 0 |
| 28 | 12 | 18 | 27 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 10 | 3 | 5 |
| 0 | 0 | 0 | 0 | 19 | 22 | 10 | 24 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 19 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 6 |
| 0 | 12 | 10 | 0 | 0 | 0 | 0 | 0 |
| 12 | 0 | 7 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 20 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 25 |
| 0 | 0 | 0 | 0 | 0 | 0 | 20 | 9 |
G:=sub<GL(8,GF(29))| [16,5,17,1,0,0,0,0,24,13,21,23,0,0,0,0,10,21,27,28,0,0,0,0,6,20,5,2,0,0,0,0,0,0,0,0,20,14,27,16,0,0,0,0,15,9,7,10,0,0,0,0,23,27,25,1,0,0,0,0,10,7,14,4],[1,0,0,14,0,0,0,0,0,1,15,25,0,0,0,0,3,25,28,0,0,0,0,0,4,0,0,28,0,0,0,0,0,0,0,0,20,14,0,0,0,0,0,0,15,9,0,0,0,0,0,0,0,0,4,28,0,0,0,0,0,0,15,25],[26,26,13,28,0,0,0,0,3,22,11,12,0,0,0,0,0,0,12,18,0,0,0,0,0,0,26,27,0,0,0,0,0,0,0,0,10,19,0,0,0,0,0,0,10,22,0,0,0,0,0,0,3,10,20,20,0,0,0,0,5,24,19,6],[0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,0,10,7,9,27,0,0,0,0,0,19,12,20,0,0,0,0,0,0,0,0,20,4,0,0,0,0,0,0,9,9,0,0,0,0,0,0,0,0,20,20,0,0,0,0,0,0,25,9] >;
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4E | 4F | ··· | 4K | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 28 | 28 | 4 | ··· | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | D14 | D14 | 2+ (1+4) | 2- (1+4) | D4⋊6D14 | D4⋊8D14 | D4.10D14 |
| kernel | C42.145D14 | C28.6Q8 | C4.D28 | C22⋊Dic14 | D14.D4 | D14⋊D4 | C22.D28 | Dic7⋊D4 | D14⋊3Q8 | C7×C4.4D4 | C4.4D4 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C14 | C14 | C2 | C2 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 3 | 3 | 12 | 3 | 3 | 2 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{145}D_{14} % in TeX
G:=Group("C4^2.145D14"); // GroupNames label
G:=SmallGroup(448,1137);
// by ID
G=gap.SmallGroup(448,1137);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,1571,570,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=b^2,a*b=b*a,c*a*c^-1=a^-1*b^2,d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b^-1,d*c*d^-1=c^13>;
// generators/relations
×
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ℤ
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