metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.153D14, C14.1332+ (1+4), (C4×D28)⋊48C2, C42.C2⋊9D7, C28⋊1D4⋊33C2, C4⋊C4.209D14, D28⋊C4⋊37C2, (C2×C28).91C23, D14.32(C4○D4), D14.5D4⋊35C2, C28.130(C4○D4), (C2×C14).239C24, (C4×C28).198C22, D14⋊C4.41C22, C4.39(Q8⋊2D7), C2.58(D4⋊8D14), (C2×D28).268C22, Dic7⋊C4.54C22, C4⋊Dic7.315C22, C22.260(C23×D7), (C4×Dic7).145C22, (C2×Dic7).124C23, (C22×D7).104C23, C7⋊10(C22.47C24), (D7×C4⋊C4)⋊39C2, C2.90(D7×C4○D4), C4⋊C4⋊7D7⋊38C2, C4⋊C4⋊D7⋊37C2, C14.201(C2×C4○D4), C2.24(C2×Q8⋊2D7), (C7×C42.C2)⋊12C2, (C2×C4×D7).129C22, (C2×C4).82(C22×D7), (C7×C4⋊C4).194C22, SmallGroup(448,1148)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1244 in 238 conjugacy classes, 97 normal (43 characteristic)
C1, C2 [×3], C2 [×5], C4 [×2], C4 [×10], C22, C22 [×13], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×12], D4 [×10], C23 [×4], D7 [×5], C14 [×3], C42, C42 [×2], C22⋊C4 [×10], C4⋊C4 [×2], C4⋊C4 [×4], C4⋊C4 [×4], C22×C4 [×6], C2×D4 [×6], Dic7 [×4], C28 [×2], C28 [×6], D14 [×2], D14 [×11], C2×C14, C2×C4⋊C4, C42⋊C2, C4×D4 [×4], C4⋊D4 [×4], C22.D4 [×2], C42.C2, C42⋊2C2 [×2], C4×D7 [×8], D28 [×10], C2×Dic7 [×2], C2×Dic7 [×2], C2×C28 [×3], C2×C28 [×4], C22×D7 [×2], C22×D7 [×2], C22.47C24, C4×Dic7 [×2], Dic7⋊C4 [×2], C4⋊Dic7 [×2], D14⋊C4 [×2], D14⋊C4 [×8], C4×C28, C7×C4⋊C4 [×2], C7×C4⋊C4 [×4], C2×C4×D7 [×2], C2×C4×D7 [×4], C2×D28 [×2], C2×D28 [×4], C4×D28 [×2], D7×C4⋊C4, C4⋊C4⋊7D7, D28⋊C4 [×2], D14.5D4 [×2], C28⋊1D4 [×2], C28⋊1D4 [×2], C4⋊C4⋊D7 [×2], C7×C42.C2, C42.153D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2+ (1+4), C22×D7 [×7], C22.47C24, Q8⋊2D7 [×2], C23×D7, C2×Q8⋊2D7, D7×C4○D4, D4⋊8D14, C42.153D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=a2b-1, dbd-1=a2b, dcd-1=c13 >
►On 224 points
Generators in S224
(1 169 212 62)(2 63 213 170)(3 171 214 64)(4 65 215 172)(5 173 216 66)(6 67 217 174)(7 175 218 68)(8 69 219 176)(9 177 220 70)(10 71 221 178)(11 179 222 72)(12 73 223 180)(13 181 224 74)(14 75 197 182)(15 183 198 76)(16 77 199 184)(17 185 200 78)(18 79 201 186)(19 187 202 80)(20 81 203 188)(21 189 204 82)(22 83 205 190)(23 191 206 84)(24 57 207 192)(25 193 208 58)(26 59 209 194)(27 195 210 60)(28 61 211 196)(29 125 148 100)(30 101 149 126)(31 127 150 102)(32 103 151 128)(33 129 152 104)(34 105 153 130)(35 131 154 106)(36 107 155 132)(37 133 156 108)(38 109 157 134)(39 135 158 110)(40 111 159 136)(41 137 160 112)(42 85 161 138)(43 139 162 86)(44 87 163 140)(45 113 164 88)(46 89 165 114)(47 115 166 90)(48 91 167 116)(49 117 168 92)(50 93 141 118)(51 119 142 94)(52 95 143 120)(53 121 144 96)(54 97 145 122)(55 123 146 98)(56 99 147 124)
(1 149 198 44)(2 164 199 31)(3 151 200 46)(4 166 201 33)(5 153 202 48)(6 168 203 35)(7 155 204 50)(8 142 205 37)(9 157 206 52)(10 144 207 39)(11 159 208 54)(12 146 209 41)(13 161 210 56)(14 148 211 43)(15 163 212 30)(16 150 213 45)(17 165 214 32)(18 152 215 47)(19 167 216 34)(20 154 217 49)(21 141 218 36)(22 156 219 51)(23 143 220 38)(24 158 221 53)(25 145 222 40)(26 160 223 55)(27 147 224 42)(28 162 197 29)(57 110 178 121)(58 97 179 136)(59 112 180 123)(60 99 181 138)(61 86 182 125)(62 101 183 140)(63 88 184 127)(64 103 185 114)(65 90 186 129)(66 105 187 116)(67 92 188 131)(68 107 189 118)(69 94 190 133)(70 109 191 120)(71 96 192 135)(72 111 193 122)(73 98 194 137)(74 85 195 124)(75 100 196 139)(76 87 169 126)(77 102 170 113)(78 89 171 128)(79 104 172 115)(80 91 173 130)(81 106 174 117)(82 93 175 132)(83 108 176 119)(84 95 177 134)
(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)
(1 197 15 211)(2 210 16 224)(3 223 17 209)(4 208 18 222)(5 221 19 207)(6 206 20 220)(7 219 21 205)(8 204 22 218)(9 217 23 203)(10 202 24 216)(11 215 25 201)(12 200 26 214)(13 213 27 199)(14 198 28 212)(29 44 43 30)(31 42 45 56)(32 55 46 41)(33 40 47 54)(34 53 48 39)(35 38 49 52)(36 51 50 37)(57 173 71 187)(58 186 72 172)(59 171 73 185)(60 184 74 170)(61 169 75 183)(62 182 76 196)(63 195 77 181)(64 180 78 194)(65 193 79 179)(66 178 80 192)(67 191 81 177)(68 176 82 190)(69 189 83 175)(70 174 84 188)(85 88 99 102)(86 101 100 87)(89 112 103 98)(90 97 104 111)(91 110 105 96)(92 95 106 109)(93 108 107 94)(113 124 127 138)(114 137 128 123)(115 122 129 136)(116 135 130 121)(117 120 131 134)(118 133 132 119)(125 140 139 126)(141 156 155 142)(143 154 157 168)(144 167 158 153)(145 152 159 166)(146 165 160 151)(147 150 161 164)(148 163 162 149)
G:=sub<Sym(224)| (1,169,212,62)(2,63,213,170)(3,171,214,64)(4,65,215,172)(5,173,216,66)(6,67,217,174)(7,175,218,68)(8,69,219,176)(9,177,220,70)(10,71,221,178)(11,179,222,72)(12,73,223,180)(13,181,224,74)(14,75,197,182)(15,183,198,76)(16,77,199,184)(17,185,200,78)(18,79,201,186)(19,187,202,80)(20,81,203,188)(21,189,204,82)(22,83,205,190)(23,191,206,84)(24,57,207,192)(25,193,208,58)(26,59,209,194)(27,195,210,60)(28,61,211,196)(29,125,148,100)(30,101,149,126)(31,127,150,102)(32,103,151,128)(33,129,152,104)(34,105,153,130)(35,131,154,106)(36,107,155,132)(37,133,156,108)(38,109,157,134)(39,135,158,110)(40,111,159,136)(41,137,160,112)(42,85,161,138)(43,139,162,86)(44,87,163,140)(45,113,164,88)(46,89,165,114)(47,115,166,90)(48,91,167,116)(49,117,168,92)(50,93,141,118)(51,119,142,94)(52,95,143,120)(53,121,144,96)(54,97,145,122)(55,123,146,98)(56,99,147,124), (1,149,198,44)(2,164,199,31)(3,151,200,46)(4,166,201,33)(5,153,202,48)(6,168,203,35)(7,155,204,50)(8,142,205,37)(9,157,206,52)(10,144,207,39)(11,159,208,54)(12,146,209,41)(13,161,210,56)(14,148,211,43)(15,163,212,30)(16,150,213,45)(17,165,214,32)(18,152,215,47)(19,167,216,34)(20,154,217,49)(21,141,218,36)(22,156,219,51)(23,143,220,38)(24,158,221,53)(25,145,222,40)(26,160,223,55)(27,147,224,42)(28,162,197,29)(57,110,178,121)(58,97,179,136)(59,112,180,123)(60,99,181,138)(61,86,182,125)(62,101,183,140)(63,88,184,127)(64,103,185,114)(65,90,186,129)(66,105,187,116)(67,92,188,131)(68,107,189,118)(69,94,190,133)(70,109,191,120)(71,96,192,135)(72,111,193,122)(73,98,194,137)(74,85,195,124)(75,100,196,139)(76,87,169,126)(77,102,170,113)(78,89,171,128)(79,104,172,115)(80,91,173,130)(81,106,174,117)(82,93,175,132)(83,108,176,119)(84,95,177,134), (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), (1,197,15,211)(2,210,16,224)(3,223,17,209)(4,208,18,222)(5,221,19,207)(6,206,20,220)(7,219,21,205)(8,204,22,218)(9,217,23,203)(10,202,24,216)(11,215,25,201)(12,200,26,214)(13,213,27,199)(14,198,28,212)(29,44,43,30)(31,42,45,56)(32,55,46,41)(33,40,47,54)(34,53,48,39)(35,38,49,52)(36,51,50,37)(57,173,71,187)(58,186,72,172)(59,171,73,185)(60,184,74,170)(61,169,75,183)(62,182,76,196)(63,195,77,181)(64,180,78,194)(65,193,79,179)(66,178,80,192)(67,191,81,177)(68,176,82,190)(69,189,83,175)(70,174,84,188)(85,88,99,102)(86,101,100,87)(89,112,103,98)(90,97,104,111)(91,110,105,96)(92,95,106,109)(93,108,107,94)(113,124,127,138)(114,137,128,123)(115,122,129,136)(116,135,130,121)(117,120,131,134)(118,133,132,119)(125,140,139,126)(141,156,155,142)(143,154,157,168)(144,167,158,153)(145,152,159,166)(146,165,160,151)(147,150,161,164)(148,163,162,149)>;
G:=Group( (1,169,212,62)(2,63,213,170)(3,171,214,64)(4,65,215,172)(5,173,216,66)(6,67,217,174)(7,175,218,68)(8,69,219,176)(9,177,220,70)(10,71,221,178)(11,179,222,72)(12,73,223,180)(13,181,224,74)(14,75,197,182)(15,183,198,76)(16,77,199,184)(17,185,200,78)(18,79,201,186)(19,187,202,80)(20,81,203,188)(21,189,204,82)(22,83,205,190)(23,191,206,84)(24,57,207,192)(25,193,208,58)(26,59,209,194)(27,195,210,60)(28,61,211,196)(29,125,148,100)(30,101,149,126)(31,127,150,102)(32,103,151,128)(33,129,152,104)(34,105,153,130)(35,131,154,106)(36,107,155,132)(37,133,156,108)(38,109,157,134)(39,135,158,110)(40,111,159,136)(41,137,160,112)(42,85,161,138)(43,139,162,86)(44,87,163,140)(45,113,164,88)(46,89,165,114)(47,115,166,90)(48,91,167,116)(49,117,168,92)(50,93,141,118)(51,119,142,94)(52,95,143,120)(53,121,144,96)(54,97,145,122)(55,123,146,98)(56,99,147,124), (1,149,198,44)(2,164,199,31)(3,151,200,46)(4,166,201,33)(5,153,202,48)(6,168,203,35)(7,155,204,50)(8,142,205,37)(9,157,206,52)(10,144,207,39)(11,159,208,54)(12,146,209,41)(13,161,210,56)(14,148,211,43)(15,163,212,30)(16,150,213,45)(17,165,214,32)(18,152,215,47)(19,167,216,34)(20,154,217,49)(21,141,218,36)(22,156,219,51)(23,143,220,38)(24,158,221,53)(25,145,222,40)(26,160,223,55)(27,147,224,42)(28,162,197,29)(57,110,178,121)(58,97,179,136)(59,112,180,123)(60,99,181,138)(61,86,182,125)(62,101,183,140)(63,88,184,127)(64,103,185,114)(65,90,186,129)(66,105,187,116)(67,92,188,131)(68,107,189,118)(69,94,190,133)(70,109,191,120)(71,96,192,135)(72,111,193,122)(73,98,194,137)(74,85,195,124)(75,100,196,139)(76,87,169,126)(77,102,170,113)(78,89,171,128)(79,104,172,115)(80,91,173,130)(81,106,174,117)(82,93,175,132)(83,108,176,119)(84,95,177,134), (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), (1,197,15,211)(2,210,16,224)(3,223,17,209)(4,208,18,222)(5,221,19,207)(6,206,20,220)(7,219,21,205)(8,204,22,218)(9,217,23,203)(10,202,24,216)(11,215,25,201)(12,200,26,214)(13,213,27,199)(14,198,28,212)(29,44,43,30)(31,42,45,56)(32,55,46,41)(33,40,47,54)(34,53,48,39)(35,38,49,52)(36,51,50,37)(57,173,71,187)(58,186,72,172)(59,171,73,185)(60,184,74,170)(61,169,75,183)(62,182,76,196)(63,195,77,181)(64,180,78,194)(65,193,79,179)(66,178,80,192)(67,191,81,177)(68,176,82,190)(69,189,83,175)(70,174,84,188)(85,88,99,102)(86,101,100,87)(89,112,103,98)(90,97,104,111)(91,110,105,96)(92,95,106,109)(93,108,107,94)(113,124,127,138)(114,137,128,123)(115,122,129,136)(116,135,130,121)(117,120,131,134)(118,133,132,119)(125,140,139,126)(141,156,155,142)(143,154,157,168)(144,167,158,153)(145,152,159,166)(146,165,160,151)(147,150,161,164)(148,163,162,149) );
G=PermutationGroup([(1,169,212,62),(2,63,213,170),(3,171,214,64),(4,65,215,172),(5,173,216,66),(6,67,217,174),(7,175,218,68),(8,69,219,176),(9,177,220,70),(10,71,221,178),(11,179,222,72),(12,73,223,180),(13,181,224,74),(14,75,197,182),(15,183,198,76),(16,77,199,184),(17,185,200,78),(18,79,201,186),(19,187,202,80),(20,81,203,188),(21,189,204,82),(22,83,205,190),(23,191,206,84),(24,57,207,192),(25,193,208,58),(26,59,209,194),(27,195,210,60),(28,61,211,196),(29,125,148,100),(30,101,149,126),(31,127,150,102),(32,103,151,128),(33,129,152,104),(34,105,153,130),(35,131,154,106),(36,107,155,132),(37,133,156,108),(38,109,157,134),(39,135,158,110),(40,111,159,136),(41,137,160,112),(42,85,161,138),(43,139,162,86),(44,87,163,140),(45,113,164,88),(46,89,165,114),(47,115,166,90),(48,91,167,116),(49,117,168,92),(50,93,141,118),(51,119,142,94),(52,95,143,120),(53,121,144,96),(54,97,145,122),(55,123,146,98),(56,99,147,124)], [(1,149,198,44),(2,164,199,31),(3,151,200,46),(4,166,201,33),(5,153,202,48),(6,168,203,35),(7,155,204,50),(8,142,205,37),(9,157,206,52),(10,144,207,39),(11,159,208,54),(12,146,209,41),(13,161,210,56),(14,148,211,43),(15,163,212,30),(16,150,213,45),(17,165,214,32),(18,152,215,47),(19,167,216,34),(20,154,217,49),(21,141,218,36),(22,156,219,51),(23,143,220,38),(24,158,221,53),(25,145,222,40),(26,160,223,55),(27,147,224,42),(28,162,197,29),(57,110,178,121),(58,97,179,136),(59,112,180,123),(60,99,181,138),(61,86,182,125),(62,101,183,140),(63,88,184,127),(64,103,185,114),(65,90,186,129),(66,105,187,116),(67,92,188,131),(68,107,189,118),(69,94,190,133),(70,109,191,120),(71,96,192,135),(72,111,193,122),(73,98,194,137),(74,85,195,124),(75,100,196,139),(76,87,169,126),(77,102,170,113),(78,89,171,128),(79,104,172,115),(80,91,173,130),(81,106,174,117),(82,93,175,132),(83,108,176,119),(84,95,177,134)], [(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)], [(1,197,15,211),(2,210,16,224),(3,223,17,209),(4,208,18,222),(5,221,19,207),(6,206,20,220),(7,219,21,205),(8,204,22,218),(9,217,23,203),(10,202,24,216),(11,215,25,201),(12,200,26,214),(13,213,27,199),(14,198,28,212),(29,44,43,30),(31,42,45,56),(32,55,46,41),(33,40,47,54),(34,53,48,39),(35,38,49,52),(36,51,50,37),(57,173,71,187),(58,186,72,172),(59,171,73,185),(60,184,74,170),(61,169,75,183),(62,182,76,196),(63,195,77,181),(64,180,78,194),(65,193,79,179),(66,178,80,192),(67,191,81,177),(68,176,82,190),(69,189,83,175),(70,174,84,188),(85,88,99,102),(86,101,100,87),(89,112,103,98),(90,97,104,111),(91,110,105,96),(92,95,106,109),(93,108,107,94),(113,124,127,138),(114,137,128,123),(115,122,129,136),(116,135,130,121),(117,120,131,134),(118,133,132,119),(125,140,139,126),(141,156,155,142),(143,154,157,168),(144,167,158,153),(145,152,159,166),(146,165,160,151),(147,150,161,164),(148,163,162,149)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 9 | 16 | 0 | 0 | 0 | 0 |
| 13 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 8 | 0 | 0 |
| 0 | 0 | 13 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 20 | 13 | 0 | 0 | 0 | 0 |
| 16 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 1 | 0 | 0 |
| 0 | 0 | 24 | 8 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
G:=sub<GL(6,GF(29))| [0,12,0,0,0,0,12,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[9,13,0,0,0,0,16,20,0,0,0,0,0,0,2,13,0,0,0,0,8,9,0,0,0,0,0,0,17,0,0,0,0,0,0,12],[20,16,0,0,0,0,13,9,0,0,0,0,0,0,21,24,0,0,0,0,1,8,0,0,0,0,0,0,17,0,0,0,0,0,0,17] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | 2+ (1+4) | Q8⋊2D7 | D7×C4○D4 | D4⋊8D14 |
| kernel | C42.153D14 | C4×D28 | D7×C4⋊C4 | C4⋊C4⋊7D7 | D28⋊C4 | D14.5D4 | C28⋊1D4 | C4⋊C4⋊D7 | C7×C42.C2 | C42.C2 | C28 | D14 | C42 | C4⋊C4 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 1 | 1 | 2 | 2 | 4 | 2 | 1 | 3 | 4 | 4 | 3 | 18 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{153}D_{14} % in TeX
G:=Group("C4^2.153D14"); // GroupNames label
G:=SmallGroup(448,1148);
// by ID
G=gap.SmallGroup(448,1148);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,387,100,1571,185,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=a^2*b^-1,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations
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