metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.91D14, C14.942+ 1+4, C14.492- 1+4, (C4×D28)⋊6C2, C4○D28⋊11C4, D28⋊27(C2×C4), C4⋊C4.310D14, (C4×Dic14)⋊8C2, C42⋊C2⋊7D7, Dic14⋊25(C2×C4), (C2×C14).67C24, (C4×C28).23C22, C28.90(C22×C4), C14.19(C23×C4), D14.6(C22×C4), Dic7⋊4D4⋊42C2, C2.2(D4⋊8D14), (C2×C28).489C23, C22⋊C4.127D14, (C22×C4).189D14, Dic7.8(C22×C4), C22.29(C23×D7), D14⋊C4.119C22, (C2×D28).286C22, C4⋊Dic7.397C22, C23.155(C22×D7), C2.2(D4.10D14), Dic7⋊C4.132C22, (C22×C28).227C22, (C22×C14).137C23, C7⋊2(C23.33C23), (C4×Dic7).195C22, (C2×Dic7).196C23, (C22×D7).164C23, (C2×Dic14).315C22, (C22×Dic7).86C22, (C2×C4)⋊7(C4×D7), C4.94(C2×C4×D7), (D7×C4⋊C4)⋊11C2, (C4×D7)⋊2(C2×C4), C7⋊D4⋊7(C2×C4), (C2×C28)⋊13(C2×C4), C22.7(C2×C4×D7), C4⋊C4⋊7D7⋊11C2, C2.21(D7×C22×C4), (C2×C4⋊Dic7)⋊39C2, (C2×C4×D7).58C22, (C7×C42⋊C2)⋊9C2, (C2×C4○D28).18C2, (C7×C4⋊C4).306C22, (C2×C14).23(C22×C4), (C2×C4).273(C22×D7), (C2×C7⋊D4).98C22, (C7×C22⋊C4).137C22, SmallGroup(448,976)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.91D14
G = < a,b,c,d | a4=b4=1, c14=d2=a2b2, ab=ba, cac-1=dad-1=a-1b2, cbc-1=a2b-1, bd=db, dcd-1=c13 >
Subgroups: 1204 in 294 conjugacy classes, 151 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C42⋊C2, C42⋊C2, C4×D4, C4×Q8, C2×C4○D4, Dic14, C4×D7, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, C23.33C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C22×Dic7, C2×C7⋊D4, C22×C28, C4×Dic14, C4×D28, Dic7⋊4D4, D7×C4⋊C4, C4⋊C4⋊7D7, C2×C4⋊Dic7, C7×C42⋊C2, C2×C4○D28, C42.91D14
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C22×C4, C24, D14, C23×C4, 2+ 1+4, 2- 1+4, C4×D7, C22×D7, C23.33C23, C2×C4×D7, C23×D7, D7×C22×C4, D4⋊8D14, D4.10D14, C42.91D14
►On 224 points
Generators in S224
(1 141 171 53)(2 156 172 40)(3 143 173 55)(4 158 174 42)(5 145 175 29)(6 160 176 44)(7 147 177 31)(8 162 178 46)(9 149 179 33)(10 164 180 48)(11 151 181 35)(12 166 182 50)(13 153 183 37)(14 168 184 52)(15 155 185 39)(16 142 186 54)(17 157 187 41)(18 144 188 56)(19 159 189 43)(20 146 190 30)(21 161 191 45)(22 148 192 32)(23 163 193 47)(24 150 194 34)(25 165 195 49)(26 152 196 36)(27 167 169 51)(28 154 170 38)(57 206 115 99)(58 221 116 86)(59 208 117 101)(60 223 118 88)(61 210 119 103)(62 197 120 90)(63 212 121 105)(64 199 122 92)(65 214 123 107)(66 201 124 94)(67 216 125 109)(68 203 126 96)(69 218 127 111)(70 205 128 98)(71 220 129 85)(72 207 130 100)(73 222 131 87)(74 209 132 102)(75 224 133 89)(76 211 134 104)(77 198 135 91)(78 213 136 106)(79 200 137 93)(80 215 138 108)(81 202 139 95)(82 217 140 110)(83 204 113 97)(84 219 114 112)
(1 103 185 224)(2 90 186 211)(3 105 187 198)(4 92 188 213)(5 107 189 200)(6 94 190 215)(7 109 191 202)(8 96 192 217)(9 111 193 204)(10 98 194 219)(11 85 195 206)(12 100 196 221)(13 87 169 208)(14 102 170 223)(15 89 171 210)(16 104 172 197)(17 91 173 212)(18 106 174 199)(19 93 175 214)(20 108 176 201)(21 95 177 216)(22 110 178 203)(23 97 179 218)(24 112 180 205)(25 99 181 220)(26 86 182 207)(27 101 183 222)(28 88 184 209)(29 123 159 79)(30 138 160 66)(31 125 161 81)(32 140 162 68)(33 127 163 83)(34 114 164 70)(35 129 165 57)(36 116 166 72)(37 131 167 59)(38 118 168 74)(39 133 141 61)(40 120 142 76)(41 135 143 63)(42 122 144 78)(43 137 145 65)(44 124 146 80)(45 139 147 67)(46 126 148 82)(47 113 149 69)(48 128 150 84)(49 115 151 71)(50 130 152 58)(51 117 153 73)(52 132 154 60)(53 119 155 75)(54 134 156 62)(55 121 157 77)(56 136 158 64)
(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 74 15 60)(2 59 16 73)(3 72 17 58)(4 57 18 71)(5 70 19 84)(6 83 20 69)(7 68 21 82)(8 81 22 67)(9 66 23 80)(10 79 24 65)(11 64 25 78)(12 77 26 63)(13 62 27 76)(14 75 28 61)(29 112 43 98)(30 97 44 111)(31 110 45 96)(32 95 46 109)(33 108 47 94)(34 93 48 107)(35 106 49 92)(36 91 50 105)(37 104 51 90)(38 89 52 103)(39 102 53 88)(40 87 54 101)(41 100 55 86)(42 85 56 99)(113 190 127 176)(114 175 128 189)(115 188 129 174)(116 173 130 187)(117 186 131 172)(118 171 132 185)(119 184 133 170)(120 169 134 183)(121 182 135 196)(122 195 136 181)(123 180 137 194)(124 193 138 179)(125 178 139 192)(126 191 140 177)(141 223 155 209)(142 208 156 222)(143 221 157 207)(144 206 158 220)(145 219 159 205)(146 204 160 218)(147 217 161 203)(148 202 162 216)(149 215 163 201)(150 200 164 214)(151 213 165 199)(152 198 166 212)(153 211 167 197)(154 224 168 210)
G:=sub<Sym(224)| (1,141,171,53)(2,156,172,40)(3,143,173,55)(4,158,174,42)(5,145,175,29)(6,160,176,44)(7,147,177,31)(8,162,178,46)(9,149,179,33)(10,164,180,48)(11,151,181,35)(12,166,182,50)(13,153,183,37)(14,168,184,52)(15,155,185,39)(16,142,186,54)(17,157,187,41)(18,144,188,56)(19,159,189,43)(20,146,190,30)(21,161,191,45)(22,148,192,32)(23,163,193,47)(24,150,194,34)(25,165,195,49)(26,152,196,36)(27,167,169,51)(28,154,170,38)(57,206,115,99)(58,221,116,86)(59,208,117,101)(60,223,118,88)(61,210,119,103)(62,197,120,90)(63,212,121,105)(64,199,122,92)(65,214,123,107)(66,201,124,94)(67,216,125,109)(68,203,126,96)(69,218,127,111)(70,205,128,98)(71,220,129,85)(72,207,130,100)(73,222,131,87)(74,209,132,102)(75,224,133,89)(76,211,134,104)(77,198,135,91)(78,213,136,106)(79,200,137,93)(80,215,138,108)(81,202,139,95)(82,217,140,110)(83,204,113,97)(84,219,114,112), (1,103,185,224)(2,90,186,211)(3,105,187,198)(4,92,188,213)(5,107,189,200)(6,94,190,215)(7,109,191,202)(8,96,192,217)(9,111,193,204)(10,98,194,219)(11,85,195,206)(12,100,196,221)(13,87,169,208)(14,102,170,223)(15,89,171,210)(16,104,172,197)(17,91,173,212)(18,106,174,199)(19,93,175,214)(20,108,176,201)(21,95,177,216)(22,110,178,203)(23,97,179,218)(24,112,180,205)(25,99,181,220)(26,86,182,207)(27,101,183,222)(28,88,184,209)(29,123,159,79)(30,138,160,66)(31,125,161,81)(32,140,162,68)(33,127,163,83)(34,114,164,70)(35,129,165,57)(36,116,166,72)(37,131,167,59)(38,118,168,74)(39,133,141,61)(40,120,142,76)(41,135,143,63)(42,122,144,78)(43,137,145,65)(44,124,146,80)(45,139,147,67)(46,126,148,82)(47,113,149,69)(48,128,150,84)(49,115,151,71)(50,130,152,58)(51,117,153,73)(52,132,154,60)(53,119,155,75)(54,134,156,62)(55,121,157,77)(56,136,158,64), (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), (1,74,15,60)(2,59,16,73)(3,72,17,58)(4,57,18,71)(5,70,19,84)(6,83,20,69)(7,68,21,82)(8,81,22,67)(9,66,23,80)(10,79,24,65)(11,64,25,78)(12,77,26,63)(13,62,27,76)(14,75,28,61)(29,112,43,98)(30,97,44,111)(31,110,45,96)(32,95,46,109)(33,108,47,94)(34,93,48,107)(35,106,49,92)(36,91,50,105)(37,104,51,90)(38,89,52,103)(39,102,53,88)(40,87,54,101)(41,100,55,86)(42,85,56,99)(113,190,127,176)(114,175,128,189)(115,188,129,174)(116,173,130,187)(117,186,131,172)(118,171,132,185)(119,184,133,170)(120,169,134,183)(121,182,135,196)(122,195,136,181)(123,180,137,194)(124,193,138,179)(125,178,139,192)(126,191,140,177)(141,223,155,209)(142,208,156,222)(143,221,157,207)(144,206,158,220)(145,219,159,205)(146,204,160,218)(147,217,161,203)(148,202,162,216)(149,215,163,201)(150,200,164,214)(151,213,165,199)(152,198,166,212)(153,211,167,197)(154,224,168,210)>;
G:=Group( (1,141,171,53)(2,156,172,40)(3,143,173,55)(4,158,174,42)(5,145,175,29)(6,160,176,44)(7,147,177,31)(8,162,178,46)(9,149,179,33)(10,164,180,48)(11,151,181,35)(12,166,182,50)(13,153,183,37)(14,168,184,52)(15,155,185,39)(16,142,186,54)(17,157,187,41)(18,144,188,56)(19,159,189,43)(20,146,190,30)(21,161,191,45)(22,148,192,32)(23,163,193,47)(24,150,194,34)(25,165,195,49)(26,152,196,36)(27,167,169,51)(28,154,170,38)(57,206,115,99)(58,221,116,86)(59,208,117,101)(60,223,118,88)(61,210,119,103)(62,197,120,90)(63,212,121,105)(64,199,122,92)(65,214,123,107)(66,201,124,94)(67,216,125,109)(68,203,126,96)(69,218,127,111)(70,205,128,98)(71,220,129,85)(72,207,130,100)(73,222,131,87)(74,209,132,102)(75,224,133,89)(76,211,134,104)(77,198,135,91)(78,213,136,106)(79,200,137,93)(80,215,138,108)(81,202,139,95)(82,217,140,110)(83,204,113,97)(84,219,114,112), (1,103,185,224)(2,90,186,211)(3,105,187,198)(4,92,188,213)(5,107,189,200)(6,94,190,215)(7,109,191,202)(8,96,192,217)(9,111,193,204)(10,98,194,219)(11,85,195,206)(12,100,196,221)(13,87,169,208)(14,102,170,223)(15,89,171,210)(16,104,172,197)(17,91,173,212)(18,106,174,199)(19,93,175,214)(20,108,176,201)(21,95,177,216)(22,110,178,203)(23,97,179,218)(24,112,180,205)(25,99,181,220)(26,86,182,207)(27,101,183,222)(28,88,184,209)(29,123,159,79)(30,138,160,66)(31,125,161,81)(32,140,162,68)(33,127,163,83)(34,114,164,70)(35,129,165,57)(36,116,166,72)(37,131,167,59)(38,118,168,74)(39,133,141,61)(40,120,142,76)(41,135,143,63)(42,122,144,78)(43,137,145,65)(44,124,146,80)(45,139,147,67)(46,126,148,82)(47,113,149,69)(48,128,150,84)(49,115,151,71)(50,130,152,58)(51,117,153,73)(52,132,154,60)(53,119,155,75)(54,134,156,62)(55,121,157,77)(56,136,158,64), (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), (1,74,15,60)(2,59,16,73)(3,72,17,58)(4,57,18,71)(5,70,19,84)(6,83,20,69)(7,68,21,82)(8,81,22,67)(9,66,23,80)(10,79,24,65)(11,64,25,78)(12,77,26,63)(13,62,27,76)(14,75,28,61)(29,112,43,98)(30,97,44,111)(31,110,45,96)(32,95,46,109)(33,108,47,94)(34,93,48,107)(35,106,49,92)(36,91,50,105)(37,104,51,90)(38,89,52,103)(39,102,53,88)(40,87,54,101)(41,100,55,86)(42,85,56,99)(113,190,127,176)(114,175,128,189)(115,188,129,174)(116,173,130,187)(117,186,131,172)(118,171,132,185)(119,184,133,170)(120,169,134,183)(121,182,135,196)(122,195,136,181)(123,180,137,194)(124,193,138,179)(125,178,139,192)(126,191,140,177)(141,223,155,209)(142,208,156,222)(143,221,157,207)(144,206,158,220)(145,219,159,205)(146,204,160,218)(147,217,161,203)(148,202,162,216)(149,215,163,201)(150,200,164,214)(151,213,165,199)(152,198,166,212)(153,211,167,197)(154,224,168,210) );
G=PermutationGroup([[(1,141,171,53),(2,156,172,40),(3,143,173,55),(4,158,174,42),(5,145,175,29),(6,160,176,44),(7,147,177,31),(8,162,178,46),(9,149,179,33),(10,164,180,48),(11,151,181,35),(12,166,182,50),(13,153,183,37),(14,168,184,52),(15,155,185,39),(16,142,186,54),(17,157,187,41),(18,144,188,56),(19,159,189,43),(20,146,190,30),(21,161,191,45),(22,148,192,32),(23,163,193,47),(24,150,194,34),(25,165,195,49),(26,152,196,36),(27,167,169,51),(28,154,170,38),(57,206,115,99),(58,221,116,86),(59,208,117,101),(60,223,118,88),(61,210,119,103),(62,197,120,90),(63,212,121,105),(64,199,122,92),(65,214,123,107),(66,201,124,94),(67,216,125,109),(68,203,126,96),(69,218,127,111),(70,205,128,98),(71,220,129,85),(72,207,130,100),(73,222,131,87),(74,209,132,102),(75,224,133,89),(76,211,134,104),(77,198,135,91),(78,213,136,106),(79,200,137,93),(80,215,138,108),(81,202,139,95),(82,217,140,110),(83,204,113,97),(84,219,114,112)], [(1,103,185,224),(2,90,186,211),(3,105,187,198),(4,92,188,213),(5,107,189,200),(6,94,190,215),(7,109,191,202),(8,96,192,217),(9,111,193,204),(10,98,194,219),(11,85,195,206),(12,100,196,221),(13,87,169,208),(14,102,170,223),(15,89,171,210),(16,104,172,197),(17,91,173,212),(18,106,174,199),(19,93,175,214),(20,108,176,201),(21,95,177,216),(22,110,178,203),(23,97,179,218),(24,112,180,205),(25,99,181,220),(26,86,182,207),(27,101,183,222),(28,88,184,209),(29,123,159,79),(30,138,160,66),(31,125,161,81),(32,140,162,68),(33,127,163,83),(34,114,164,70),(35,129,165,57),(36,116,166,72),(37,131,167,59),(38,118,168,74),(39,133,141,61),(40,120,142,76),(41,135,143,63),(42,122,144,78),(43,137,145,65),(44,124,146,80),(45,139,147,67),(46,126,148,82),(47,113,149,69),(48,128,150,84),(49,115,151,71),(50,130,152,58),(51,117,153,73),(52,132,154,60),(53,119,155,75),(54,134,156,62),(55,121,157,77),(56,136,158,64)], [(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)], [(1,74,15,60),(2,59,16,73),(3,72,17,58),(4,57,18,71),(5,70,19,84),(6,83,20,69),(7,68,21,82),(8,81,22,67),(9,66,23,80),(10,79,24,65),(11,64,25,78),(12,77,26,63),(13,62,27,76),(14,75,28,61),(29,112,43,98),(30,97,44,111),(31,110,45,96),(32,95,46,109),(33,108,47,94),(34,93,48,107),(35,106,49,92),(36,91,50,105),(37,104,51,90),(38,89,52,103),(39,102,53,88),(40,87,54,101),(41,100,55,86),(42,85,56,99),(113,190,127,176),(114,175,128,189),(115,188,129,174),(116,173,130,187),(117,186,131,172),(118,171,132,185),(119,184,133,170),(120,169,134,183),(121,182,135,196),(122,195,136,181),(123,180,137,194),(124,193,138,179),(125,178,139,192),(126,191,140,177),(141,223,155,209),(142,208,156,222),(143,221,157,207),(144,206,158,220),(145,219,159,205),(146,204,160,218),(147,217,161,203),(148,202,162,216),(149,215,163,201),(150,200,164,214),(151,213,165,199),(152,198,166,212),(153,211,167,197),(154,224,168,210)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4L | 4M | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28AP |
| order | 1 | 2 | 2 | 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 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D7 | D14 | D14 | D14 | D14 | C4×D7 | 2+ 1+4 | 2- 1+4 | D4⋊8D14 | D4.10D14 |
| kernel | C42.91D14 | C4×Dic14 | C4×D28 | Dic7⋊4D4 | D7×C4⋊C4 | C4⋊C4⋊7D7 | C2×C4⋊Dic7 | C7×C42⋊C2 | C2×C4○D28 | C4○D28 | C42⋊C2 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×C4 | C14 | C14 | C2 | C2 |
| # reps | 1 | 2 | 2 | 4 | 2 | 2 | 1 | 1 | 1 | 16 | 3 | 6 | 6 | 6 | 3 | 24 | 1 | 1 | 6 | 6 |
Matrix representation of C42.91D14 ►in GL6(𝔽29)
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 2 | 27 | 9 |
| 0 | 0 | 17 | 5 | 4 | 0 |
| 0 | 0 | 0 | 14 | 18 | 27 |
| 0 | 0 | 3 | 16 | 2 | 11 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 16 | 18 |
| 0 | 0 | 0 | 17 | 23 | 20 |
| 0 | 0 | 15 | 1 | 12 | 0 |
| 0 | 0 | 19 | 12 | 0 | 12 |
| 3 | 8 | 0 | 0 | 0 | 0 |
| 21 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 26 | 6 | 8 |
| 0 | 0 | 18 | 12 | 11 | 11 |
| 0 | 0 | 0 | 0 | 26 | 3 |
| 0 | 0 | 0 | 0 | 26 | 22 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 28 | 13 | 9 |
| 0 | 0 | 5 | 21 | 28 | 1 |
| 0 | 0 | 21 | 14 | 4 | 4 |
| 0 | 0 | 21 | 12 | 18 | 25 |
G:=sub<GL(6,GF(29))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,24,17,0,3,0,0,2,5,14,16,0,0,27,4,18,2,0,0,9,0,27,11],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,17,0,15,19,0,0,0,17,1,12,0,0,16,23,12,0,0,0,18,20,0,12],[3,21,0,0,0,0,8,8,0,0,0,0,0,0,27,18,0,0,0,0,26,12,0,0,0,0,6,11,26,26,0,0,8,11,3,22],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,8,5,21,21,0,0,28,21,14,12,0,0,13,28,4,18,0,0,9,1,4,25] >;
C42.91D14 in GAP, Magma, Sage, TeX
C_4^2._{91}D_{14} % in TeX
G:=Group("C4^2.91D14"); // GroupNames label
G:=SmallGroup(448,976);
// by ID
G=gap.SmallGroup(448,976);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,570,297,80,18822]);
// 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*b^2,c*b*c^-1=a^2*b^-1,b*d=d*b,d*c*d^-1=c^13>;
// generators/relations