metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.122D14, C14.72- (1+4), (C4×Q8)⋊5D7, (Q8×C28)⋊5C2, C4⋊C4.291D14, D14⋊Q8⋊10C2, (C4×Dic14)⋊36C2, Dic7⋊Q8⋊9C2, C4.18(C4○D28), C42⋊2D7⋊17C2, C42⋊D7⋊33C2, (C2×Q8).176D14, Dic7⋊3Q8⋊17C2, D28⋊C4.10C2, C28.116(C4○D4), (C4×C28).238C22, (C2×C28).621C23, (C2×C14).112C24, D14⋊C4.68C22, C28.23D4.7C2, C4.D28.10C2, Dic7.21(C4○D4), (C2×D28).140C22, Dic7⋊C4.68C22, C4⋊Dic7.303C22, (Q8×C14).212C22, (C4×Dic7).81C22, (C22×D7).44C23, C22.137(C23×D7), C7⋊3(C22.50C24), (C2×Dic7).211C23, C2.10(Q8.10D14), (C2×Dic14).147C22, C2.27(D7×C4○D4), C4⋊C4⋊D7⋊10C2, C14.53(C2×C4○D4), C2.60(C2×C4○D28), (C2×C4×D7).206C22, (C7×C4⋊C4).340C22, (C2×C4).653(C22×D7), SmallGroup(448,1021)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 900 in 212 conjugacy classes, 97 normal (43 characteristic)
C1, C2 [×3], C2 [×2], C4 [×2], C4 [×13], C22, C22 [×6], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×10], D4 [×2], Q8 [×6], C23 [×2], D7 [×2], C14 [×3], C42, C42 [×2], C42 [×4], C22⋊C4 [×10], C4⋊C4, C4⋊C4 [×2], C4⋊C4 [×9], C22×C4 [×2], C2×D4, C2×Q8, C2×Q8 [×2], Dic7 [×2], Dic7 [×5], C28 [×2], C28 [×6], D14 [×6], C2×C14, C42⋊C2 [×2], C4×D4, C4×Q8, C4×Q8 [×2], C22⋊Q8 [×2], C4.4D4 [×2], C42⋊2C2 [×4], C4⋊Q8, Dic14 [×4], C4×D7 [×4], D28 [×2], C2×Dic7 [×4], C2×Dic7 [×2], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×2], C22×D7 [×2], C22.50C24, C4×Dic7 [×2], C4×Dic7 [×2], Dic7⋊C4 [×2], Dic7⋊C4 [×6], C4⋊Dic7, D14⋊C4 [×10], C4×C28, C4×C28 [×2], C7×C4⋊C4, C7×C4⋊C4 [×2], C2×Dic14 [×2], C2×C4×D7 [×2], C2×D28, Q8×C14, C4×Dic14, C42⋊D7 [×2], C4.D28, C42⋊2D7 [×2], Dic7⋊3Q8, D28⋊C4, D14⋊Q8 [×2], C4⋊C4⋊D7 [×2], Dic7⋊Q8, C28.23D4, Q8×C28, C42.122D14
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], C22.50C24, C4○D28 [×2], C23×D7, C2×C4○D28, Q8.10D14, D7×C4○D4, C42.122D14
Generators and relations
G = < a,b,c,d | a4=b4=d2=1, c14=b2, ab=ba, ac=ca, dad=ab2, cbc-1=dbd=a2b-1, dcd=c13 >
►On 224 points
Generators in S224
(1 106 140 169)(2 107 113 170)(3 108 114 171)(4 109 115 172)(5 110 116 173)(6 111 117 174)(7 112 118 175)(8 85 119 176)(9 86 120 177)(10 87 121 178)(11 88 122 179)(12 89 123 180)(13 90 124 181)(14 91 125 182)(15 92 126 183)(16 93 127 184)(17 94 128 185)(18 95 129 186)(19 96 130 187)(20 97 131 188)(21 98 132 189)(22 99 133 190)(23 100 134 191)(24 101 135 192)(25 102 136 193)(26 103 137 194)(27 104 138 195)(28 105 139 196)(29 204 154 66)(30 205 155 67)(31 206 156 68)(32 207 157 69)(33 208 158 70)(34 209 159 71)(35 210 160 72)(36 211 161 73)(37 212 162 74)(38 213 163 75)(39 214 164 76)(40 215 165 77)(41 216 166 78)(42 217 167 79)(43 218 168 80)(44 219 141 81)(45 220 142 82)(46 221 143 83)(47 222 144 84)(48 223 145 57)(49 224 146 58)(50 197 147 59)(51 198 148 60)(52 199 149 61)(53 200 150 62)(54 201 151 63)(55 202 152 64)(56 203 153 65)
(1 31 15 45)(2 143 16 157)(3 33 17 47)(4 145 18 159)(5 35 19 49)(6 147 20 161)(7 37 21 51)(8 149 22 163)(9 39 23 53)(10 151 24 165)(11 41 25 55)(12 153 26 167)(13 43 27 29)(14 155 28 141)(30 139 44 125)(32 113 46 127)(34 115 48 129)(36 117 50 131)(38 119 52 133)(40 121 54 135)(42 123 56 137)(57 95 71 109)(58 173 72 187)(59 97 73 111)(60 175 74 189)(61 99 75 85)(62 177 76 191)(63 101 77 87)(64 179 78 193)(65 103 79 89)(66 181 80 195)(67 105 81 91)(68 183 82 169)(69 107 83 93)(70 185 84 171)(86 214 100 200)(88 216 102 202)(90 218 104 204)(92 220 106 206)(94 222 108 208)(96 224 110 210)(98 198 112 212)(114 158 128 144)(116 160 130 146)(118 162 132 148)(120 164 134 150)(122 166 136 152)(124 168 138 154)(126 142 140 156)(170 221 184 207)(172 223 186 209)(174 197 188 211)(176 199 190 213)(178 201 192 215)(180 203 194 217)(182 205 196 219)
(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 21)(2 6)(3 19)(5 17)(7 15)(8 28)(9 13)(10 26)(12 24)(14 22)(16 20)(23 27)(29 164)(30 149)(31 162)(32 147)(33 160)(34 145)(35 158)(36 143)(37 156)(38 141)(39 154)(40 167)(41 152)(42 165)(43 150)(44 163)(45 148)(46 161)(47 146)(48 159)(49 144)(50 157)(51 142)(52 155)(53 168)(54 153)(55 166)(56 151)(57 223)(58 208)(59 221)(60 206)(61 219)(62 204)(63 217)(64 202)(65 215)(66 200)(67 213)(68 198)(69 211)(70 224)(71 209)(72 222)(73 207)(74 220)(75 205)(76 218)(77 203)(78 216)(79 201)(80 214)(81 199)(82 212)(83 197)(84 210)(85 91)(86 104)(87 89)(88 102)(90 100)(92 98)(93 111)(94 96)(95 109)(97 107)(99 105)(101 103)(106 112)(108 110)(113 117)(114 130)(116 128)(118 126)(119 139)(120 124)(121 137)(123 135)(125 133)(127 131)(132 140)(134 138)(169 175)(170 188)(171 173)(172 186)(174 184)(176 182)(177 195)(178 180)(179 193)(181 191)(183 189)(185 187)(190 196)(192 194)
G:=sub<Sym(224)| (1,106,140,169)(2,107,113,170)(3,108,114,171)(4,109,115,172)(5,110,116,173)(6,111,117,174)(7,112,118,175)(8,85,119,176)(9,86,120,177)(10,87,121,178)(11,88,122,179)(12,89,123,180)(13,90,124,181)(14,91,125,182)(15,92,126,183)(16,93,127,184)(17,94,128,185)(18,95,129,186)(19,96,130,187)(20,97,131,188)(21,98,132,189)(22,99,133,190)(23,100,134,191)(24,101,135,192)(25,102,136,193)(26,103,137,194)(27,104,138,195)(28,105,139,196)(29,204,154,66)(30,205,155,67)(31,206,156,68)(32,207,157,69)(33,208,158,70)(34,209,159,71)(35,210,160,72)(36,211,161,73)(37,212,162,74)(38,213,163,75)(39,214,164,76)(40,215,165,77)(41,216,166,78)(42,217,167,79)(43,218,168,80)(44,219,141,81)(45,220,142,82)(46,221,143,83)(47,222,144,84)(48,223,145,57)(49,224,146,58)(50,197,147,59)(51,198,148,60)(52,199,149,61)(53,200,150,62)(54,201,151,63)(55,202,152,64)(56,203,153,65), (1,31,15,45)(2,143,16,157)(3,33,17,47)(4,145,18,159)(5,35,19,49)(6,147,20,161)(7,37,21,51)(8,149,22,163)(9,39,23,53)(10,151,24,165)(11,41,25,55)(12,153,26,167)(13,43,27,29)(14,155,28,141)(30,139,44,125)(32,113,46,127)(34,115,48,129)(36,117,50,131)(38,119,52,133)(40,121,54,135)(42,123,56,137)(57,95,71,109)(58,173,72,187)(59,97,73,111)(60,175,74,189)(61,99,75,85)(62,177,76,191)(63,101,77,87)(64,179,78,193)(65,103,79,89)(66,181,80,195)(67,105,81,91)(68,183,82,169)(69,107,83,93)(70,185,84,171)(86,214,100,200)(88,216,102,202)(90,218,104,204)(92,220,106,206)(94,222,108,208)(96,224,110,210)(98,198,112,212)(114,158,128,144)(116,160,130,146)(118,162,132,148)(120,164,134,150)(122,166,136,152)(124,168,138,154)(126,142,140,156)(170,221,184,207)(172,223,186,209)(174,197,188,211)(176,199,190,213)(178,201,192,215)(180,203,194,217)(182,205,196,219), (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), (1,21)(2,6)(3,19)(5,17)(7,15)(8,28)(9,13)(10,26)(12,24)(14,22)(16,20)(23,27)(29,164)(30,149)(31,162)(32,147)(33,160)(34,145)(35,158)(36,143)(37,156)(38,141)(39,154)(40,167)(41,152)(42,165)(43,150)(44,163)(45,148)(46,161)(47,146)(48,159)(49,144)(50,157)(51,142)(52,155)(53,168)(54,153)(55,166)(56,151)(57,223)(58,208)(59,221)(60,206)(61,219)(62,204)(63,217)(64,202)(65,215)(66,200)(67,213)(68,198)(69,211)(70,224)(71,209)(72,222)(73,207)(74,220)(75,205)(76,218)(77,203)(78,216)(79,201)(80,214)(81,199)(82,212)(83,197)(84,210)(85,91)(86,104)(87,89)(88,102)(90,100)(92,98)(93,111)(94,96)(95,109)(97,107)(99,105)(101,103)(106,112)(108,110)(113,117)(114,130)(116,128)(118,126)(119,139)(120,124)(121,137)(123,135)(125,133)(127,131)(132,140)(134,138)(169,175)(170,188)(171,173)(172,186)(174,184)(176,182)(177,195)(178,180)(179,193)(181,191)(183,189)(185,187)(190,196)(192,194)>;
G:=Group( (1,106,140,169)(2,107,113,170)(3,108,114,171)(4,109,115,172)(5,110,116,173)(6,111,117,174)(7,112,118,175)(8,85,119,176)(9,86,120,177)(10,87,121,178)(11,88,122,179)(12,89,123,180)(13,90,124,181)(14,91,125,182)(15,92,126,183)(16,93,127,184)(17,94,128,185)(18,95,129,186)(19,96,130,187)(20,97,131,188)(21,98,132,189)(22,99,133,190)(23,100,134,191)(24,101,135,192)(25,102,136,193)(26,103,137,194)(27,104,138,195)(28,105,139,196)(29,204,154,66)(30,205,155,67)(31,206,156,68)(32,207,157,69)(33,208,158,70)(34,209,159,71)(35,210,160,72)(36,211,161,73)(37,212,162,74)(38,213,163,75)(39,214,164,76)(40,215,165,77)(41,216,166,78)(42,217,167,79)(43,218,168,80)(44,219,141,81)(45,220,142,82)(46,221,143,83)(47,222,144,84)(48,223,145,57)(49,224,146,58)(50,197,147,59)(51,198,148,60)(52,199,149,61)(53,200,150,62)(54,201,151,63)(55,202,152,64)(56,203,153,65), (1,31,15,45)(2,143,16,157)(3,33,17,47)(4,145,18,159)(5,35,19,49)(6,147,20,161)(7,37,21,51)(8,149,22,163)(9,39,23,53)(10,151,24,165)(11,41,25,55)(12,153,26,167)(13,43,27,29)(14,155,28,141)(30,139,44,125)(32,113,46,127)(34,115,48,129)(36,117,50,131)(38,119,52,133)(40,121,54,135)(42,123,56,137)(57,95,71,109)(58,173,72,187)(59,97,73,111)(60,175,74,189)(61,99,75,85)(62,177,76,191)(63,101,77,87)(64,179,78,193)(65,103,79,89)(66,181,80,195)(67,105,81,91)(68,183,82,169)(69,107,83,93)(70,185,84,171)(86,214,100,200)(88,216,102,202)(90,218,104,204)(92,220,106,206)(94,222,108,208)(96,224,110,210)(98,198,112,212)(114,158,128,144)(116,160,130,146)(118,162,132,148)(120,164,134,150)(122,166,136,152)(124,168,138,154)(126,142,140,156)(170,221,184,207)(172,223,186,209)(174,197,188,211)(176,199,190,213)(178,201,192,215)(180,203,194,217)(182,205,196,219), (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), (1,21)(2,6)(3,19)(5,17)(7,15)(8,28)(9,13)(10,26)(12,24)(14,22)(16,20)(23,27)(29,164)(30,149)(31,162)(32,147)(33,160)(34,145)(35,158)(36,143)(37,156)(38,141)(39,154)(40,167)(41,152)(42,165)(43,150)(44,163)(45,148)(46,161)(47,146)(48,159)(49,144)(50,157)(51,142)(52,155)(53,168)(54,153)(55,166)(56,151)(57,223)(58,208)(59,221)(60,206)(61,219)(62,204)(63,217)(64,202)(65,215)(66,200)(67,213)(68,198)(69,211)(70,224)(71,209)(72,222)(73,207)(74,220)(75,205)(76,218)(77,203)(78,216)(79,201)(80,214)(81,199)(82,212)(83,197)(84,210)(85,91)(86,104)(87,89)(88,102)(90,100)(92,98)(93,111)(94,96)(95,109)(97,107)(99,105)(101,103)(106,112)(108,110)(113,117)(114,130)(116,128)(118,126)(119,139)(120,124)(121,137)(123,135)(125,133)(127,131)(132,140)(134,138)(169,175)(170,188)(171,173)(172,186)(174,184)(176,182)(177,195)(178,180)(179,193)(181,191)(183,189)(185,187)(190,196)(192,194) );
G=PermutationGroup([(1,106,140,169),(2,107,113,170),(3,108,114,171),(4,109,115,172),(5,110,116,173),(6,111,117,174),(7,112,118,175),(8,85,119,176),(9,86,120,177),(10,87,121,178),(11,88,122,179),(12,89,123,180),(13,90,124,181),(14,91,125,182),(15,92,126,183),(16,93,127,184),(17,94,128,185),(18,95,129,186),(19,96,130,187),(20,97,131,188),(21,98,132,189),(22,99,133,190),(23,100,134,191),(24,101,135,192),(25,102,136,193),(26,103,137,194),(27,104,138,195),(28,105,139,196),(29,204,154,66),(30,205,155,67),(31,206,156,68),(32,207,157,69),(33,208,158,70),(34,209,159,71),(35,210,160,72),(36,211,161,73),(37,212,162,74),(38,213,163,75),(39,214,164,76),(40,215,165,77),(41,216,166,78),(42,217,167,79),(43,218,168,80),(44,219,141,81),(45,220,142,82),(46,221,143,83),(47,222,144,84),(48,223,145,57),(49,224,146,58),(50,197,147,59),(51,198,148,60),(52,199,149,61),(53,200,150,62),(54,201,151,63),(55,202,152,64),(56,203,153,65)], [(1,31,15,45),(2,143,16,157),(3,33,17,47),(4,145,18,159),(5,35,19,49),(6,147,20,161),(7,37,21,51),(8,149,22,163),(9,39,23,53),(10,151,24,165),(11,41,25,55),(12,153,26,167),(13,43,27,29),(14,155,28,141),(30,139,44,125),(32,113,46,127),(34,115,48,129),(36,117,50,131),(38,119,52,133),(40,121,54,135),(42,123,56,137),(57,95,71,109),(58,173,72,187),(59,97,73,111),(60,175,74,189),(61,99,75,85),(62,177,76,191),(63,101,77,87),(64,179,78,193),(65,103,79,89),(66,181,80,195),(67,105,81,91),(68,183,82,169),(69,107,83,93),(70,185,84,171),(86,214,100,200),(88,216,102,202),(90,218,104,204),(92,220,106,206),(94,222,108,208),(96,224,110,210),(98,198,112,212),(114,158,128,144),(116,160,130,146),(118,162,132,148),(120,164,134,150),(122,166,136,152),(124,168,138,154),(126,142,140,156),(170,221,184,207),(172,223,186,209),(174,197,188,211),(176,199,190,213),(178,201,192,215),(180,203,194,217),(182,205,196,219)], [(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)], [(1,21),(2,6),(3,19),(5,17),(7,15),(8,28),(9,13),(10,26),(12,24),(14,22),(16,20),(23,27),(29,164),(30,149),(31,162),(32,147),(33,160),(34,145),(35,158),(36,143),(37,156),(38,141),(39,154),(40,167),(41,152),(42,165),(43,150),(44,163),(45,148),(46,161),(47,146),(48,159),(49,144),(50,157),(51,142),(52,155),(53,168),(54,153),(55,166),(56,151),(57,223),(58,208),(59,221),(60,206),(61,219),(62,204),(63,217),(64,202),(65,215),(66,200),(67,213),(68,198),(69,211),(70,224),(71,209),(72,222),(73,207),(74,220),(75,205),(76,218),(77,203),(78,216),(79,201),(80,214),(81,199),(82,212),(83,197),(84,210),(85,91),(86,104),(87,89),(88,102),(90,100),(92,98),(93,111),(94,96),(95,109),(97,107),(99,105),(101,103),(106,112),(108,110),(113,117),(114,130),(116,128),(118,126),(119,139),(120,124),(121,137),(123,135),(125,133),(127,131),(132,140),(134,138),(169,175),(170,188),(171,173),(172,186),(174,184),(176,182),(177,195),(178,180),(179,193),(181,191),(183,189),(185,187),(190,196),(192,194)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 13 | 0 | 0 |
| 0 | 0 | 4 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 2 |
| 0 | 0 | 0 | 0 | 1 | 12 |
| 10 | 10 | 0 | 0 | 0 | 0 |
| 19 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 12 | 28 |
| 10 | 10 | 0 | 0 | 0 | 0 |
| 22 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 24 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 12 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,18,4,0,0,0,0,13,11,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,1,0,0,0,0,2,12],[10,19,0,0,0,0,10,22,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,1,12,0,0,0,0,0,28],[10,22,0,0,0,0,10,19,0,0,0,0,0,0,1,24,0,0,0,0,0,28,0,0,0,0,0,0,1,12,0,0,0,0,0,28] >;
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28L | 28M | ··· | 28AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | C4○D28 | 2- (1+4) | Q8.10D14 | D7×C4○D4 |
| kernel | C42.122D14 | C4×Dic14 | C42⋊D7 | C4.D28 | C42⋊2D7 | Dic7⋊3Q8 | D28⋊C4 | D14⋊Q8 | C4⋊C4⋊D7 | Dic7⋊Q8 | C28.23D4 | Q8×C28 | C4×Q8 | Dic7 | C28 | C42 | C4⋊C4 | C2×Q8 | C4 | C14 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 3 | 4 | 4 | 9 | 9 | 3 | 24 | 1 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_4^2._{122}D_{14} % in TeX
G:=Group("C4^2.122D14"); // GroupNames label
G:=SmallGroup(448,1021);
// by ID
G=gap.SmallGroup(448,1021);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,232,758,100,794,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=d^2=1,c^14=b^2,a*b=b*a,a*c=c*a,d*a*d=a*b^2,c*b*c^-1=d*b*d=a^2*b^-1,d*c*d=c^13>;
// generators/relations
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