metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.233D14, (C4×D7)⋊6D4, C4.30(D4×D7), D14.6(C2×D4), C28.59(C2×D4), (D7×C42)⋊8C2, C28⋊D4⋊23C2, C4.4D4⋊18D7, D14⋊D4⋊37C2, Dic7⋊3(C4○D4), (C2×D4).168D14, C4.D28⋊22C2, (C2×C28).76C23, (C2×Q8).134D14, C22⋊C4.70D14, Dic7.65(C2×D4), C14.86(C22×D4), Dic7⋊Q8⋊19C2, Dic7⋊4D4⋊27C2, (C4×C28).182C22, (C2×C14).212C24, D14⋊C4.58C22, C23.34(C22×D7), (C2×D28).160C22, (D4×C14).150C22, Dic7⋊C4.47C22, (C22×C14).42C23, C7⋊4(C22.26C24), (Q8×C14).121C22, C22.233(C23×D7), (C4×Dic7).296C22, (C2×Dic7).249C23, (C22×D7).212C23, (C2×Dic14).173C22, (C22×Dic7).137C22, C2.59(C2×D4×D7), C2.71(D7×C4○D4), (C2×Q8⋊2D7)⋊9C2, (C7×C4.4D4)⋊6C2, (C2×D4⋊2D7)⋊18C2, C14.183(C2×C4○D4), (C2×C4×D7).118C22, (C2×C4).298(C22×D7), (C2×C7⋊D4).55C22, (C7×C22⋊C4).59C22, SmallGroup(448,1121)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1516 in 310 conjugacy classes, 107 normal (29 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×2], C4 [×12], C22, C22 [×16], C7, C2×C4, C2×C4 [×4], C2×C4 [×21], D4 [×20], Q8 [×4], C23 [×2], C23 [×3], D7 [×4], C14, C14 [×2], C14 [×2], C42, C42 [×3], C22⋊C4 [×4], C22⋊C4 [×4], C4⋊C4 [×4], C22×C4 [×7], C2×D4, C2×D4 [×9], C2×Q8, C2×Q8, C4○D4 [×8], Dic7 [×6], Dic7 [×2], C28 [×2], C28 [×4], D14 [×2], D14 [×8], C2×C14, C2×C14 [×6], C2×C42, C4×D4 [×4], C4⋊D4 [×4], C4.4D4, C4.4D4, C4⋊1D4, C4⋊Q8, C2×C4○D4 [×2], Dic14 [×2], C4×D7 [×4], C4×D7 [×8], D28 [×6], C2×Dic7, C2×Dic7 [×4], C2×Dic7 [×4], C7⋊D4 [×12], C2×C28, C2×C28 [×4], C7×D4 [×2], C7×Q8 [×2], C22×D7, C22×D7 [×2], C22×C14 [×2], C22.26C24, C4×Dic7, C4×Dic7 [×2], Dic7⋊C4 [×4], D14⋊C4 [×4], C4×C28, C7×C22⋊C4 [×4], C2×Dic14, C2×C4×D7, C2×C4×D7 [×4], C2×D28, C2×D28 [×2], D4⋊2D7 [×4], Q8⋊2D7 [×4], C22×Dic7 [×2], C2×C7⋊D4 [×6], D4×C14, Q8×C14, D7×C42, C4.D28, Dic7⋊4D4 [×4], D14⋊D4 [×4], C28⋊D4, Dic7⋊Q8, C7×C4.4D4, C2×D4⋊2D7, C2×Q8⋊2D7, C42.233D14
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×4], C24, D14 [×7], C22×D4, C2×C4○D4 [×2], C22×D7 [×7], C22.26C24, D4×D7 [×2], C23×D7, C2×D4×D7, D7×C4○D4 [×2], C42.233D14
Generators and relations
G = < a,b,c,d | a4=b4=c14=d2=1, ab=ba, cac-1=dad=ab2, cbc-1=dbd=a2b, dcd=a2c-1 >
►On 224 points
Generators in S224
(1 214 102 138)(2 170 103 74)(3 216 104 140)(4 172 105 76)(5 218 106 128)(6 174 107 78)(7 220 108 130)(8 176 109 80)(9 222 110 132)(10 178 111 82)(11 224 112 134)(12 180 99 84)(13 212 100 136)(14 182 101 72)(15 145 208 96)(16 162 209 46)(17 147 210 98)(18 164 197 48)(19 149 198 86)(20 166 199 50)(21 151 200 88)(22 168 201 52)(23 153 202 90)(24 156 203 54)(25 141 204 92)(26 158 205 56)(27 143 206 94)(28 160 207 44)(29 95 68 144)(30 45 69 161)(31 97 70 146)(32 47 57 163)(33 85 58 148)(34 49 59 165)(35 87 60 150)(36 51 61 167)(37 89 62 152)(38 53 63 155)(39 91 64 154)(40 55 65 157)(41 93 66 142)(42 43 67 159)(71 195 181 116)(73 183 169 118)(75 185 171 120)(77 187 173 122)(79 189 175 124)(81 191 177 126)(83 193 179 114)(113 133 192 223)(115 135 194 211)(117 137 196 213)(119 139 184 215)(121 127 186 217)(123 129 188 219)(125 131 190 221)
(1 203 183 39)(2 25 184 65)(3 205 185 41)(4 27 186 67)(5 207 187 29)(6 15 188 69)(7 209 189 31)(8 17 190 57)(9 197 191 33)(10 19 192 59)(11 199 193 35)(12 21 194 61)(13 201 195 37)(14 23 196 63)(16 124 70 108)(18 126 58 110)(20 114 60 112)(22 116 62 100)(24 118 64 102)(26 120 66 104)(28 122 68 106)(30 107 208 123)(32 109 210 125)(34 111 198 113)(36 99 200 115)(38 101 202 117)(40 103 204 119)(42 105 206 121)(43 76 94 127)(44 173 95 218)(45 78 96 129)(46 175 97 220)(47 80 98 131)(48 177 85 222)(49 82 86 133)(50 179 87 224)(51 84 88 135)(52 181 89 212)(53 72 90 137)(54 169 91 214)(55 74 92 139)(56 171 93 216)(71 152 136 168)(73 154 138 156)(75 142 140 158)(77 144 128 160)(79 146 130 162)(81 148 132 164)(83 150 134 166)(141 215 157 170)(143 217 159 172)(145 219 161 174)(147 221 163 176)(149 223 165 178)(151 211 167 180)(153 213 155 182)
(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)
(1 213)(2 136)(3 211)(4 134)(5 223)(6 132)(7 221)(8 130)(9 219)(10 128)(11 217)(12 140)(13 215)(14 138)(15 48)(16 163)(17 46)(18 161)(19 44)(20 159)(21 56)(22 157)(23 54)(24 155)(25 52)(26 167)(27 50)(28 165)(29 86)(30 148)(31 98)(32 146)(33 96)(34 144)(35 94)(36 142)(37 92)(38 154)(39 90)(40 152)(41 88)(42 150)(43 199)(45 197)(47 209)(49 207)(51 205)(53 203)(55 201)(57 97)(58 145)(59 95)(60 143)(61 93)(62 141)(63 91)(64 153)(65 89)(66 151)(67 87)(68 149)(69 85)(70 147)(71 184)(72 118)(73 196)(74 116)(75 194)(76 114)(77 192)(78 126)(79 190)(80 124)(81 188)(82 122)(83 186)(84 120)(99 216)(100 139)(101 214)(102 137)(103 212)(104 135)(105 224)(106 133)(107 222)(108 131)(109 220)(110 129)(111 218)(112 127)(113 173)(115 171)(117 169)(119 181)(121 179)(123 177)(125 175)(156 202)(158 200)(160 198)(162 210)(164 208)(166 206)(168 204)(170 195)(172 193)(174 191)(176 189)(178 187)(180 185)(182 183)
G:=sub<Sym(224)| (1,214,102,138)(2,170,103,74)(3,216,104,140)(4,172,105,76)(5,218,106,128)(6,174,107,78)(7,220,108,130)(8,176,109,80)(9,222,110,132)(10,178,111,82)(11,224,112,134)(12,180,99,84)(13,212,100,136)(14,182,101,72)(15,145,208,96)(16,162,209,46)(17,147,210,98)(18,164,197,48)(19,149,198,86)(20,166,199,50)(21,151,200,88)(22,168,201,52)(23,153,202,90)(24,156,203,54)(25,141,204,92)(26,158,205,56)(27,143,206,94)(28,160,207,44)(29,95,68,144)(30,45,69,161)(31,97,70,146)(32,47,57,163)(33,85,58,148)(34,49,59,165)(35,87,60,150)(36,51,61,167)(37,89,62,152)(38,53,63,155)(39,91,64,154)(40,55,65,157)(41,93,66,142)(42,43,67,159)(71,195,181,116)(73,183,169,118)(75,185,171,120)(77,187,173,122)(79,189,175,124)(81,191,177,126)(83,193,179,114)(113,133,192,223)(115,135,194,211)(117,137,196,213)(119,139,184,215)(121,127,186,217)(123,129,188,219)(125,131,190,221), (1,203,183,39)(2,25,184,65)(3,205,185,41)(4,27,186,67)(5,207,187,29)(6,15,188,69)(7,209,189,31)(8,17,190,57)(9,197,191,33)(10,19,192,59)(11,199,193,35)(12,21,194,61)(13,201,195,37)(14,23,196,63)(16,124,70,108)(18,126,58,110)(20,114,60,112)(22,116,62,100)(24,118,64,102)(26,120,66,104)(28,122,68,106)(30,107,208,123)(32,109,210,125)(34,111,198,113)(36,99,200,115)(38,101,202,117)(40,103,204,119)(42,105,206,121)(43,76,94,127)(44,173,95,218)(45,78,96,129)(46,175,97,220)(47,80,98,131)(48,177,85,222)(49,82,86,133)(50,179,87,224)(51,84,88,135)(52,181,89,212)(53,72,90,137)(54,169,91,214)(55,74,92,139)(56,171,93,216)(71,152,136,168)(73,154,138,156)(75,142,140,158)(77,144,128,160)(79,146,130,162)(81,148,132,164)(83,150,134,166)(141,215,157,170)(143,217,159,172)(145,219,161,174)(147,221,163,176)(149,223,165,178)(151,211,167,180)(153,213,155,182), (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), (1,213)(2,136)(3,211)(4,134)(5,223)(6,132)(7,221)(8,130)(9,219)(10,128)(11,217)(12,140)(13,215)(14,138)(15,48)(16,163)(17,46)(18,161)(19,44)(20,159)(21,56)(22,157)(23,54)(24,155)(25,52)(26,167)(27,50)(28,165)(29,86)(30,148)(31,98)(32,146)(33,96)(34,144)(35,94)(36,142)(37,92)(38,154)(39,90)(40,152)(41,88)(42,150)(43,199)(45,197)(47,209)(49,207)(51,205)(53,203)(55,201)(57,97)(58,145)(59,95)(60,143)(61,93)(62,141)(63,91)(64,153)(65,89)(66,151)(67,87)(68,149)(69,85)(70,147)(71,184)(72,118)(73,196)(74,116)(75,194)(76,114)(77,192)(78,126)(79,190)(80,124)(81,188)(82,122)(83,186)(84,120)(99,216)(100,139)(101,214)(102,137)(103,212)(104,135)(105,224)(106,133)(107,222)(108,131)(109,220)(110,129)(111,218)(112,127)(113,173)(115,171)(117,169)(119,181)(121,179)(123,177)(125,175)(156,202)(158,200)(160,198)(162,210)(164,208)(166,206)(168,204)(170,195)(172,193)(174,191)(176,189)(178,187)(180,185)(182,183)>;
G:=Group( (1,214,102,138)(2,170,103,74)(3,216,104,140)(4,172,105,76)(5,218,106,128)(6,174,107,78)(7,220,108,130)(8,176,109,80)(9,222,110,132)(10,178,111,82)(11,224,112,134)(12,180,99,84)(13,212,100,136)(14,182,101,72)(15,145,208,96)(16,162,209,46)(17,147,210,98)(18,164,197,48)(19,149,198,86)(20,166,199,50)(21,151,200,88)(22,168,201,52)(23,153,202,90)(24,156,203,54)(25,141,204,92)(26,158,205,56)(27,143,206,94)(28,160,207,44)(29,95,68,144)(30,45,69,161)(31,97,70,146)(32,47,57,163)(33,85,58,148)(34,49,59,165)(35,87,60,150)(36,51,61,167)(37,89,62,152)(38,53,63,155)(39,91,64,154)(40,55,65,157)(41,93,66,142)(42,43,67,159)(71,195,181,116)(73,183,169,118)(75,185,171,120)(77,187,173,122)(79,189,175,124)(81,191,177,126)(83,193,179,114)(113,133,192,223)(115,135,194,211)(117,137,196,213)(119,139,184,215)(121,127,186,217)(123,129,188,219)(125,131,190,221), (1,203,183,39)(2,25,184,65)(3,205,185,41)(4,27,186,67)(5,207,187,29)(6,15,188,69)(7,209,189,31)(8,17,190,57)(9,197,191,33)(10,19,192,59)(11,199,193,35)(12,21,194,61)(13,201,195,37)(14,23,196,63)(16,124,70,108)(18,126,58,110)(20,114,60,112)(22,116,62,100)(24,118,64,102)(26,120,66,104)(28,122,68,106)(30,107,208,123)(32,109,210,125)(34,111,198,113)(36,99,200,115)(38,101,202,117)(40,103,204,119)(42,105,206,121)(43,76,94,127)(44,173,95,218)(45,78,96,129)(46,175,97,220)(47,80,98,131)(48,177,85,222)(49,82,86,133)(50,179,87,224)(51,84,88,135)(52,181,89,212)(53,72,90,137)(54,169,91,214)(55,74,92,139)(56,171,93,216)(71,152,136,168)(73,154,138,156)(75,142,140,158)(77,144,128,160)(79,146,130,162)(81,148,132,164)(83,150,134,166)(141,215,157,170)(143,217,159,172)(145,219,161,174)(147,221,163,176)(149,223,165,178)(151,211,167,180)(153,213,155,182), (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), (1,213)(2,136)(3,211)(4,134)(5,223)(6,132)(7,221)(8,130)(9,219)(10,128)(11,217)(12,140)(13,215)(14,138)(15,48)(16,163)(17,46)(18,161)(19,44)(20,159)(21,56)(22,157)(23,54)(24,155)(25,52)(26,167)(27,50)(28,165)(29,86)(30,148)(31,98)(32,146)(33,96)(34,144)(35,94)(36,142)(37,92)(38,154)(39,90)(40,152)(41,88)(42,150)(43,199)(45,197)(47,209)(49,207)(51,205)(53,203)(55,201)(57,97)(58,145)(59,95)(60,143)(61,93)(62,141)(63,91)(64,153)(65,89)(66,151)(67,87)(68,149)(69,85)(70,147)(71,184)(72,118)(73,196)(74,116)(75,194)(76,114)(77,192)(78,126)(79,190)(80,124)(81,188)(82,122)(83,186)(84,120)(99,216)(100,139)(101,214)(102,137)(103,212)(104,135)(105,224)(106,133)(107,222)(108,131)(109,220)(110,129)(111,218)(112,127)(113,173)(115,171)(117,169)(119,181)(121,179)(123,177)(125,175)(156,202)(158,200)(160,198)(162,210)(164,208)(166,206)(168,204)(170,195)(172,193)(174,191)(176,189)(178,187)(180,185)(182,183) );
G=PermutationGroup([(1,214,102,138),(2,170,103,74),(3,216,104,140),(4,172,105,76),(5,218,106,128),(6,174,107,78),(7,220,108,130),(8,176,109,80),(9,222,110,132),(10,178,111,82),(11,224,112,134),(12,180,99,84),(13,212,100,136),(14,182,101,72),(15,145,208,96),(16,162,209,46),(17,147,210,98),(18,164,197,48),(19,149,198,86),(20,166,199,50),(21,151,200,88),(22,168,201,52),(23,153,202,90),(24,156,203,54),(25,141,204,92),(26,158,205,56),(27,143,206,94),(28,160,207,44),(29,95,68,144),(30,45,69,161),(31,97,70,146),(32,47,57,163),(33,85,58,148),(34,49,59,165),(35,87,60,150),(36,51,61,167),(37,89,62,152),(38,53,63,155),(39,91,64,154),(40,55,65,157),(41,93,66,142),(42,43,67,159),(71,195,181,116),(73,183,169,118),(75,185,171,120),(77,187,173,122),(79,189,175,124),(81,191,177,126),(83,193,179,114),(113,133,192,223),(115,135,194,211),(117,137,196,213),(119,139,184,215),(121,127,186,217),(123,129,188,219),(125,131,190,221)], [(1,203,183,39),(2,25,184,65),(3,205,185,41),(4,27,186,67),(5,207,187,29),(6,15,188,69),(7,209,189,31),(8,17,190,57),(9,197,191,33),(10,19,192,59),(11,199,193,35),(12,21,194,61),(13,201,195,37),(14,23,196,63),(16,124,70,108),(18,126,58,110),(20,114,60,112),(22,116,62,100),(24,118,64,102),(26,120,66,104),(28,122,68,106),(30,107,208,123),(32,109,210,125),(34,111,198,113),(36,99,200,115),(38,101,202,117),(40,103,204,119),(42,105,206,121),(43,76,94,127),(44,173,95,218),(45,78,96,129),(46,175,97,220),(47,80,98,131),(48,177,85,222),(49,82,86,133),(50,179,87,224),(51,84,88,135),(52,181,89,212),(53,72,90,137),(54,169,91,214),(55,74,92,139),(56,171,93,216),(71,152,136,168),(73,154,138,156),(75,142,140,158),(77,144,128,160),(79,146,130,162),(81,148,132,164),(83,150,134,166),(141,215,157,170),(143,217,159,172),(145,219,161,174),(147,221,163,176),(149,223,165,178),(151,211,167,180),(153,213,155,182)], [(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)], [(1,213),(2,136),(3,211),(4,134),(5,223),(6,132),(7,221),(8,130),(9,219),(10,128),(11,217),(12,140),(13,215),(14,138),(15,48),(16,163),(17,46),(18,161),(19,44),(20,159),(21,56),(22,157),(23,54),(24,155),(25,52),(26,167),(27,50),(28,165),(29,86),(30,148),(31,98),(32,146),(33,96),(34,144),(35,94),(36,142),(37,92),(38,154),(39,90),(40,152),(41,88),(42,150),(43,199),(45,197),(47,209),(49,207),(51,205),(53,203),(55,201),(57,97),(58,145),(59,95),(60,143),(61,93),(62,141),(63,91),(64,153),(65,89),(66,151),(67,87),(68,149),(69,85),(70,147),(71,184),(72,118),(73,196),(74,116),(75,194),(76,114),(77,192),(78,126),(79,190),(80,124),(81,188),(82,122),(83,186),(84,120),(99,216),(100,139),(101,214),(102,137),(103,212),(104,135),(105,224),(106,133),(107,222),(108,131),(109,220),(110,129),(111,218),(112,127),(113,173),(115,171),(117,169),(119,181),(121,179),(123,177),(125,175),(156,202),(158,200),(160,198),(162,210),(164,208),(166,206),(168,204),(170,195),(172,193),(174,191),(176,189),(178,187),(180,185),(182,183)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 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 | 28 | 0 |
| 0 | 0 | 0 | 0 | 27 | 1 |
| 25 | 19 | 0 | 0 | 0 | 0 |
| 15 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 17 |
| 0 | 0 | 0 | 0 | 24 | 17 |
| 11 | 22 | 0 | 0 | 0 | 0 |
| 13 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 28 |
| 0 | 0 | 0 | 0 | 0 | 28 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,28,27,0,0,0,0,0,1],[25,15,0,0,0,0,19,1,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,12,24,0,0,0,0,17,17],[11,13,0,0,0,0,22,18,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,28,28] >;
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 4P | 4Q | 4R | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 4 | 4 | 14 | 14 | 28 | 28 | 2 | ··· | 2 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D4×D7 | D7×C4○D4 |
| kernel | C42.233D14 | D7×C42 | C4.D28 | Dic7⋊4D4 | D14⋊D4 | C28⋊D4 | Dic7⋊Q8 | C7×C4.4D4 | C2×D4⋊2D7 | C2×Q8⋊2D7 | C4×D7 | C4.4D4 | Dic7 | C42 | C22⋊C4 | C2×D4 | C2×Q8 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 4 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 8 | 3 | 12 | 3 | 3 | 6 | 12 |
In GAP, Magma, Sage, TeX
C_4^2._{233}D_{14} % in TeX
G:=Group("C4^2.233D14"); // GroupNames label
G:=SmallGroup(448,1121);
// by ID
G=gap.SmallGroup(448,1121);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,232,100,1123,346,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=d^2=1,a*b=b*a,c*a*c^-1=d*a*d=a*b^2,c*b*c^-1=d*b*d=a^2*b,d*c*d=a^2*c^-1>;
// generators/relations
×
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ℤ
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