metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.179D14, C14.852+ (1+4), C4⋊Q8⋊17D7, (C4×D28)⋊52C2, C28⋊1D4⋊41C2, C4⋊C4.222D14, (C2×Q8).89D14, C28.141(C4○D4), C28.23D4⋊28C2, (C4×C28).219C22, (C2×C28).640C23, (C2×C14).278C24, D14⋊C4.53C22, C4.42(Q8⋊2D7), C2.89(D4⋊6D14), (C2×D28).275C22, C4⋊Dic7.387C22, (Q8×C14).145C22, C22.299(C23×D7), C7⋊5(C22.49C24), (C2×Dic7).275C23, (C4×Dic7).167C22, (C22×D7).123C23, (C7×C4⋊Q8)⋊20C2, C4⋊C4⋊7D7⋊44C2, C14.125(C2×C4○D4), C2.33(C2×Q8⋊2D7), (C2×C4×D7).151C22, (C7×C4⋊C4).221C22, (C2×C4).603(C22×D7), SmallGroup(448,1187)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1196 in 236 conjugacy classes, 99 normal (13 characteristic)
C1, C2, C2 [×2], C2 [×4], C4 [×4], C4 [×9], C22, C22 [×12], C7, C2×C4, C2×C4 [×6], C2×C4 [×12], D4 [×8], Q8 [×2], C23 [×4], D7 [×4], C14, C14 [×2], C42, C42 [×4], C22⋊C4 [×12], C4⋊C4 [×4], C4⋊C4 [×2], C22×C4 [×4], C2×D4 [×6], C2×Q8 [×2], Dic7 [×4], C28 [×4], C28 [×5], D14 [×12], C2×C14, C42⋊C2 [×4], C4×D4 [×2], C4⋊D4 [×4], C4.4D4 [×4], C4⋊Q8, C4×D7 [×8], D28 [×8], C2×Dic7 [×4], C2×C28, C2×C28 [×6], C7×Q8 [×2], C22×D7 [×4], C22.49C24, C4×Dic7 [×4], C4⋊Dic7 [×2], D14⋊C4 [×12], C4×C28, C7×C4⋊C4 [×4], C2×C4×D7 [×4], C2×D28 [×6], Q8×C14 [×2], C4×D28 [×2], C4⋊C4⋊7D7 [×4], C28⋊1D4 [×4], C28.23D4 [×4], C7×C4⋊Q8, C42.179D14
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], C22.49C24, Q8⋊2D7 [×4], C23×D7, D4⋊6D14, C2×Q8⋊2D7 [×2], C42.179D14
Generators and relations
G = < a,b,c,d | a4=b4=1, c14=b2, d2=a2b2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b, dcd-1=a2c13 >
►On 224 points
Generators in S224
(1 109 47 139)(2 140 48 110)(3 111 49 113)(4 114 50 112)(5 85 51 115)(6 116 52 86)(7 87 53 117)(8 118 54 88)(9 89 55 119)(10 120 56 90)(11 91 29 121)(12 122 30 92)(13 93 31 123)(14 124 32 94)(15 95 33 125)(16 126 34 96)(17 97 35 127)(18 128 36 98)(19 99 37 129)(20 130 38 100)(21 101 39 131)(22 132 40 102)(23 103 41 133)(24 134 42 104)(25 105 43 135)(26 136 44 106)(27 107 45 137)(28 138 46 108)(57 222 171 144)(58 145 172 223)(59 224 173 146)(60 147 174 197)(61 198 175 148)(62 149 176 199)(63 200 177 150)(64 151 178 201)(65 202 179 152)(66 153 180 203)(67 204 181 154)(68 155 182 205)(69 206 183 156)(70 157 184 207)(71 208 185 158)(72 159 186 209)(73 210 187 160)(74 161 188 211)(75 212 189 162)(76 163 190 213)(77 214 191 164)(78 165 192 215)(79 216 193 166)(80 167 194 217)(81 218 195 168)(82 141 196 219)(83 220 169 142)(84 143 170 221)
(1 71 15 57)(2 58 16 72)(3 73 17 59)(4 60 18 74)(5 75 19 61)(6 62 20 76)(7 77 21 63)(8 64 22 78)(9 79 23 65)(10 66 24 80)(11 81 25 67)(12 68 26 82)(13 83 27 69)(14 70 28 84)(29 195 43 181)(30 182 44 196)(31 169 45 183)(32 184 46 170)(33 171 47 185)(34 186 48 172)(35 173 49 187)(36 188 50 174)(37 175 51 189)(38 190 52 176)(39 177 53 191)(40 192 54 178)(41 179 55 193)(42 194 56 180)(85 212 99 198)(86 199 100 213)(87 214 101 200)(88 201 102 215)(89 216 103 202)(90 203 104 217)(91 218 105 204)(92 205 106 219)(93 220 107 206)(94 207 108 221)(95 222 109 208)(96 209 110 223)(97 224 111 210)(98 211 112 197)(113 160 127 146)(114 147 128 161)(115 162 129 148)(116 149 130 163)(117 164 131 150)(118 151 132 165)(119 166 133 152)(120 153 134 167)(121 168 135 154)(122 155 136 141)(123 142 137 156)(124 157 138 143)(125 144 139 158)(126 159 140 145)
(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)
(1 157 33 221)(2 220 34 156)(3 155 35 219)(4 218 36 154)(5 153 37 217)(6 216 38 152)(7 151 39 215)(8 214 40 150)(9 149 41 213)(10 212 42 148)(11 147 43 211)(12 210 44 146)(13 145 45 209)(14 208 46 144)(15 143 47 207)(16 206 48 142)(17 141 49 205)(18 204 50 168)(19 167 51 203)(20 202 52 166)(21 165 53 201)(22 200 54 164)(23 163 55 199)(24 198 56 162)(25 161 29 197)(26 224 30 160)(27 159 31 223)(28 222 32 158)(57 94 185 138)(58 137 186 93)(59 92 187 136)(60 135 188 91)(61 90 189 134)(62 133 190 89)(63 88 191 132)(64 131 192 87)(65 86 193 130)(66 129 194 85)(67 112 195 128)(68 127 196 111)(69 110 169 126)(70 125 170 109)(71 108 171 124)(72 123 172 107)(73 106 173 122)(74 121 174 105)(75 104 175 120)(76 119 176 103)(77 102 177 118)(78 117 178 101)(79 100 179 116)(80 115 180 99)(81 98 181 114)(82 113 182 97)(83 96 183 140)(84 139 184 95)
G:=sub<Sym(224)| (1,109,47,139)(2,140,48,110)(3,111,49,113)(4,114,50,112)(5,85,51,115)(6,116,52,86)(7,87,53,117)(8,118,54,88)(9,89,55,119)(10,120,56,90)(11,91,29,121)(12,122,30,92)(13,93,31,123)(14,124,32,94)(15,95,33,125)(16,126,34,96)(17,97,35,127)(18,128,36,98)(19,99,37,129)(20,130,38,100)(21,101,39,131)(22,132,40,102)(23,103,41,133)(24,134,42,104)(25,105,43,135)(26,136,44,106)(27,107,45,137)(28,138,46,108)(57,222,171,144)(58,145,172,223)(59,224,173,146)(60,147,174,197)(61,198,175,148)(62,149,176,199)(63,200,177,150)(64,151,178,201)(65,202,179,152)(66,153,180,203)(67,204,181,154)(68,155,182,205)(69,206,183,156)(70,157,184,207)(71,208,185,158)(72,159,186,209)(73,210,187,160)(74,161,188,211)(75,212,189,162)(76,163,190,213)(77,214,191,164)(78,165,192,215)(79,216,193,166)(80,167,194,217)(81,218,195,168)(82,141,196,219)(83,220,169,142)(84,143,170,221), (1,71,15,57)(2,58,16,72)(3,73,17,59)(4,60,18,74)(5,75,19,61)(6,62,20,76)(7,77,21,63)(8,64,22,78)(9,79,23,65)(10,66,24,80)(11,81,25,67)(12,68,26,82)(13,83,27,69)(14,70,28,84)(29,195,43,181)(30,182,44,196)(31,169,45,183)(32,184,46,170)(33,171,47,185)(34,186,48,172)(35,173,49,187)(36,188,50,174)(37,175,51,189)(38,190,52,176)(39,177,53,191)(40,192,54,178)(41,179,55,193)(42,194,56,180)(85,212,99,198)(86,199,100,213)(87,214,101,200)(88,201,102,215)(89,216,103,202)(90,203,104,217)(91,218,105,204)(92,205,106,219)(93,220,107,206)(94,207,108,221)(95,222,109,208)(96,209,110,223)(97,224,111,210)(98,211,112,197)(113,160,127,146)(114,147,128,161)(115,162,129,148)(116,149,130,163)(117,164,131,150)(118,151,132,165)(119,166,133,152)(120,153,134,167)(121,168,135,154)(122,155,136,141)(123,142,137,156)(124,157,138,143)(125,144,139,158)(126,159,140,145), (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), (1,157,33,221)(2,220,34,156)(3,155,35,219)(4,218,36,154)(5,153,37,217)(6,216,38,152)(7,151,39,215)(8,214,40,150)(9,149,41,213)(10,212,42,148)(11,147,43,211)(12,210,44,146)(13,145,45,209)(14,208,46,144)(15,143,47,207)(16,206,48,142)(17,141,49,205)(18,204,50,168)(19,167,51,203)(20,202,52,166)(21,165,53,201)(22,200,54,164)(23,163,55,199)(24,198,56,162)(25,161,29,197)(26,224,30,160)(27,159,31,223)(28,222,32,158)(57,94,185,138)(58,137,186,93)(59,92,187,136)(60,135,188,91)(61,90,189,134)(62,133,190,89)(63,88,191,132)(64,131,192,87)(65,86,193,130)(66,129,194,85)(67,112,195,128)(68,127,196,111)(69,110,169,126)(70,125,170,109)(71,108,171,124)(72,123,172,107)(73,106,173,122)(74,121,174,105)(75,104,175,120)(76,119,176,103)(77,102,177,118)(78,117,178,101)(79,100,179,116)(80,115,180,99)(81,98,181,114)(82,113,182,97)(83,96,183,140)(84,139,184,95)>;
G:=Group( (1,109,47,139)(2,140,48,110)(3,111,49,113)(4,114,50,112)(5,85,51,115)(6,116,52,86)(7,87,53,117)(8,118,54,88)(9,89,55,119)(10,120,56,90)(11,91,29,121)(12,122,30,92)(13,93,31,123)(14,124,32,94)(15,95,33,125)(16,126,34,96)(17,97,35,127)(18,128,36,98)(19,99,37,129)(20,130,38,100)(21,101,39,131)(22,132,40,102)(23,103,41,133)(24,134,42,104)(25,105,43,135)(26,136,44,106)(27,107,45,137)(28,138,46,108)(57,222,171,144)(58,145,172,223)(59,224,173,146)(60,147,174,197)(61,198,175,148)(62,149,176,199)(63,200,177,150)(64,151,178,201)(65,202,179,152)(66,153,180,203)(67,204,181,154)(68,155,182,205)(69,206,183,156)(70,157,184,207)(71,208,185,158)(72,159,186,209)(73,210,187,160)(74,161,188,211)(75,212,189,162)(76,163,190,213)(77,214,191,164)(78,165,192,215)(79,216,193,166)(80,167,194,217)(81,218,195,168)(82,141,196,219)(83,220,169,142)(84,143,170,221), (1,71,15,57)(2,58,16,72)(3,73,17,59)(4,60,18,74)(5,75,19,61)(6,62,20,76)(7,77,21,63)(8,64,22,78)(9,79,23,65)(10,66,24,80)(11,81,25,67)(12,68,26,82)(13,83,27,69)(14,70,28,84)(29,195,43,181)(30,182,44,196)(31,169,45,183)(32,184,46,170)(33,171,47,185)(34,186,48,172)(35,173,49,187)(36,188,50,174)(37,175,51,189)(38,190,52,176)(39,177,53,191)(40,192,54,178)(41,179,55,193)(42,194,56,180)(85,212,99,198)(86,199,100,213)(87,214,101,200)(88,201,102,215)(89,216,103,202)(90,203,104,217)(91,218,105,204)(92,205,106,219)(93,220,107,206)(94,207,108,221)(95,222,109,208)(96,209,110,223)(97,224,111,210)(98,211,112,197)(113,160,127,146)(114,147,128,161)(115,162,129,148)(116,149,130,163)(117,164,131,150)(118,151,132,165)(119,166,133,152)(120,153,134,167)(121,168,135,154)(122,155,136,141)(123,142,137,156)(124,157,138,143)(125,144,139,158)(126,159,140,145), (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), (1,157,33,221)(2,220,34,156)(3,155,35,219)(4,218,36,154)(5,153,37,217)(6,216,38,152)(7,151,39,215)(8,214,40,150)(9,149,41,213)(10,212,42,148)(11,147,43,211)(12,210,44,146)(13,145,45,209)(14,208,46,144)(15,143,47,207)(16,206,48,142)(17,141,49,205)(18,204,50,168)(19,167,51,203)(20,202,52,166)(21,165,53,201)(22,200,54,164)(23,163,55,199)(24,198,56,162)(25,161,29,197)(26,224,30,160)(27,159,31,223)(28,222,32,158)(57,94,185,138)(58,137,186,93)(59,92,187,136)(60,135,188,91)(61,90,189,134)(62,133,190,89)(63,88,191,132)(64,131,192,87)(65,86,193,130)(66,129,194,85)(67,112,195,128)(68,127,196,111)(69,110,169,126)(70,125,170,109)(71,108,171,124)(72,123,172,107)(73,106,173,122)(74,121,174,105)(75,104,175,120)(76,119,176,103)(77,102,177,118)(78,117,178,101)(79,100,179,116)(80,115,180,99)(81,98,181,114)(82,113,182,97)(83,96,183,140)(84,139,184,95) );
G=PermutationGroup([(1,109,47,139),(2,140,48,110),(3,111,49,113),(4,114,50,112),(5,85,51,115),(6,116,52,86),(7,87,53,117),(8,118,54,88),(9,89,55,119),(10,120,56,90),(11,91,29,121),(12,122,30,92),(13,93,31,123),(14,124,32,94),(15,95,33,125),(16,126,34,96),(17,97,35,127),(18,128,36,98),(19,99,37,129),(20,130,38,100),(21,101,39,131),(22,132,40,102),(23,103,41,133),(24,134,42,104),(25,105,43,135),(26,136,44,106),(27,107,45,137),(28,138,46,108),(57,222,171,144),(58,145,172,223),(59,224,173,146),(60,147,174,197),(61,198,175,148),(62,149,176,199),(63,200,177,150),(64,151,178,201),(65,202,179,152),(66,153,180,203),(67,204,181,154),(68,155,182,205),(69,206,183,156),(70,157,184,207),(71,208,185,158),(72,159,186,209),(73,210,187,160),(74,161,188,211),(75,212,189,162),(76,163,190,213),(77,214,191,164),(78,165,192,215),(79,216,193,166),(80,167,194,217),(81,218,195,168),(82,141,196,219),(83,220,169,142),(84,143,170,221)], [(1,71,15,57),(2,58,16,72),(3,73,17,59),(4,60,18,74),(5,75,19,61),(6,62,20,76),(7,77,21,63),(8,64,22,78),(9,79,23,65),(10,66,24,80),(11,81,25,67),(12,68,26,82),(13,83,27,69),(14,70,28,84),(29,195,43,181),(30,182,44,196),(31,169,45,183),(32,184,46,170),(33,171,47,185),(34,186,48,172),(35,173,49,187),(36,188,50,174),(37,175,51,189),(38,190,52,176),(39,177,53,191),(40,192,54,178),(41,179,55,193),(42,194,56,180),(85,212,99,198),(86,199,100,213),(87,214,101,200),(88,201,102,215),(89,216,103,202),(90,203,104,217),(91,218,105,204),(92,205,106,219),(93,220,107,206),(94,207,108,221),(95,222,109,208),(96,209,110,223),(97,224,111,210),(98,211,112,197),(113,160,127,146),(114,147,128,161),(115,162,129,148),(116,149,130,163),(117,164,131,150),(118,151,132,165),(119,166,133,152),(120,153,134,167),(121,168,135,154),(122,155,136,141),(123,142,137,156),(124,157,138,143),(125,144,139,158),(126,159,140,145)], [(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)], [(1,157,33,221),(2,220,34,156),(3,155,35,219),(4,218,36,154),(5,153,37,217),(6,216,38,152),(7,151,39,215),(8,214,40,150),(9,149,41,213),(10,212,42,148),(11,147,43,211),(12,210,44,146),(13,145,45,209),(14,208,46,144),(15,143,47,207),(16,206,48,142),(17,141,49,205),(18,204,50,168),(19,167,51,203),(20,202,52,166),(21,165,53,201),(22,200,54,164),(23,163,55,199),(24,198,56,162),(25,161,29,197),(26,224,30,160),(27,159,31,223),(28,222,32,158),(57,94,185,138),(58,137,186,93),(59,92,187,136),(60,135,188,91),(61,90,189,134),(62,133,190,89),(63,88,191,132),(64,131,192,87),(65,86,193,130),(66,129,194,85),(67,112,195,128),(68,127,196,111),(69,110,169,126),(70,125,170,109),(71,108,171,124),(72,123,172,107),(73,106,173,122),(74,121,174,105),(75,104,175,120),(76,119,176,103),(77,102,177,118),(78,117,178,101),(79,100,179,116),(80,115,180,99),(81,98,181,114),(82,113,182,97),(83,96,183,140),(84,139,184,95)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 5 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 19 | 0 | 0 |
| 0 | 0 | 10 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 27 |
| 0 | 0 | 0 | 0 | 1 | 28 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[12,0,0,0,0,0,0,17,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,5,17],[0,12,0,0,0,0,12,0,0,0,0,0,0,0,7,10,0,0,0,0,19,19,0,0,0,0,0,0,1,1,0,0,0,0,27,28],[0,17,0,0,0,0,12,0,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2+ (1+4) | Q8⋊2D7 | D4⋊6D14 |
| kernel | C42.179D14 | C4×D28 | C4⋊C4⋊7D7 | C28⋊1D4 | C28.23D4 | C7×C4⋊Q8 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C2 |
| # reps | 1 | 2 | 4 | 4 | 4 | 1 | 3 | 8 | 3 | 12 | 6 | 1 | 12 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{179}D_{14} % in TeX
G:=Group("C4^2.179D14"); // GroupNames label
G:=SmallGroup(448,1187);
// by ID
G=gap.SmallGroup(448,1187);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,387,100,675,570,185,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=b^2,d^2=a^2*b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=a^2*c^13>;
// generators/relations
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