metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊C4.178D14, (D4×Dic7)⋊16C2, C4⋊D4.10D7, (C2×D4).152D14, C22⋊C4.47D14, C28.3Q8⋊18C2, Dic7⋊3Q8⋊21C2, C28.201(C4○D4), C28.17D4⋊15C2, C28.48D4⋊31C2, C4.67(D4⋊2D7), (C2×C14).144C24, (C2×C28).501C23, (C22×C4).367D14, C23.11(C22×D7), Dic7.41(C4○D4), (D4×C14).118C22, C23.18D14⋊7C2, C23.D14⋊14C2, C22.5(D4⋊2D7), C23.11D14⋊4C2, Dic7⋊C4.15C22, C4⋊Dic7.205C22, (C22×C14).15C23, (C4×Dic7).91C22, C22.165(C23×D7), C23.D7.21C22, (C22×C28).238C22, C7⋊6(C23.36C23), (C2×Dic7).226C23, (C2×Dic14).152C22, (C22×Dic7).105C22, (C2×C4×Dic7)⋊8C2, C2.35(D7×C4○D4), (C7×C4⋊D4).7C2, C14.149(C2×C4○D4), C2.32(C2×D4⋊2D7), (C2×C14).20(C4○D4), (C7×C4⋊C4).140C22, (C2×C4).292(C22×D7), (C7×C22⋊C4).9C22, SmallGroup(448,1053)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4.178D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b2, bab-1=a-1, ac=ca, ad=da, cbc-1=dbd-1=b-1, dcd-1=c-1 >
Subgroups: 844 in 234 conjugacy classes, 101 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C2×C42, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, Dic14, C2×Dic7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C23.36C23, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C22×Dic7, C22×Dic7, C22×C28, D4×C14, D4×C14, C23.11D14, C23.D14, Dic7⋊3Q8, C28.3Q8, C2×C4×Dic7, C28.48D4, D4×Dic7, D4×Dic7, C23.18D14, C28.17D4, C7×C4⋊D4, C4⋊C4.178D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, C22×D7, C23.36C23, D4⋊2D7, C23×D7, C2×D4⋊2D7, D7×C4○D4, C4⋊C4.178D14
►On 224 points
Generators in S224
(1 218 101 27)(2 219 102 28)(3 220 103 15)(4 221 104 16)(5 222 105 17)(6 223 106 18)(7 224 107 19)(8 211 108 20)(9 212 109 21)(10 213 110 22)(11 214 111 23)(12 215 112 24)(13 216 99 25)(14 217 100 26)(29 150 139 198)(30 151 140 199)(31 152 127 200)(32 153 128 201)(33 154 129 202)(34 141 130 203)(35 142 131 204)(36 143 132 205)(37 144 133 206)(38 145 134 207)(39 146 135 208)(40 147 136 209)(41 148 137 210)(42 149 138 197)(43 61 50 68)(44 62 51 69)(45 63 52 70)(46 64 53 57)(47 65 54 58)(48 66 55 59)(49 67 56 60)(71 122 78 115)(72 123 79 116)(73 124 80 117)(74 125 81 118)(75 126 82 119)(76 113 83 120)(77 114 84 121)(85 180 92 173)(86 181 93 174)(87 182 94 175)(88 169 95 176)(89 170 96 177)(90 171 97 178)(91 172 98 179)(155 193 162 186)(156 194 163 187)(157 195 164 188)(158 196 165 189)(159 183 166 190)(160 184 167 191)(161 185 168 192)
(1 124 108 93)(2 94 109 125)(3 126 110 95)(4 96 111 113)(5 114 112 97)(6 98 99 115)(7 116 100 85)(8 86 101 117)(9 118 102 87)(10 88 103 119)(11 120 104 89)(12 90 105 121)(13 122 106 91)(14 92 107 123)(15 82 213 176)(16 177 214 83)(17 84 215 178)(18 179 216 71)(19 72 217 180)(20 181 218 73)(21 74 219 182)(22 169 220 75)(23 76 221 170)(24 171 222 77)(25 78 223 172)(26 173 224 79)(27 80 211 174)(28 175 212 81)(29 187 132 57)(30 58 133 188)(31 189 134 59)(32 60 135 190)(33 191 136 61)(34 62 137 192)(35 193 138 63)(36 64 139 194)(37 195 140 65)(38 66 127 196)(39 183 128 67)(40 68 129 184)(41 185 130 69)(42 70 131 186)(43 154 167 209)(44 210 168 141)(45 142 155 197)(46 198 156 143)(47 144 157 199)(48 200 158 145)(49 146 159 201)(50 202 160 147)(51 148 161 203)(52 204 162 149)(53 150 163 205)(54 206 164 151)(55 152 165 207)(56 208 166 153)
(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)
(1 139 8 132)(2 138 9 131)(3 137 10 130)(4 136 11 129)(5 135 12 128)(6 134 13 127)(7 133 14 140)(15 148 22 141)(16 147 23 154)(17 146 24 153)(18 145 25 152)(19 144 26 151)(20 143 27 150)(21 142 28 149)(29 108 36 101)(30 107 37 100)(31 106 38 99)(32 105 39 112)(33 104 40 111)(34 103 41 110)(35 102 42 109)(43 177 160 76)(44 176 161 75)(45 175 162 74)(46 174 163 73)(47 173 164 72)(48 172 165 71)(49 171 166 84)(50 170 167 83)(51 169 168 82)(52 182 155 81)(53 181 156 80)(54 180 157 79)(55 179 158 78)(56 178 159 77)(57 93 194 117)(58 92 195 116)(59 91 196 115)(60 90 183 114)(61 89 184 113)(62 88 185 126)(63 87 186 125)(64 86 187 124)(65 85 188 123)(66 98 189 122)(67 97 190 121)(68 96 191 120)(69 95 192 119)(70 94 193 118)(197 212 204 219)(198 211 205 218)(199 224 206 217)(200 223 207 216)(201 222 208 215)(202 221 209 214)(203 220 210 213)
G:=sub<Sym(224)| (1,218,101,27)(2,219,102,28)(3,220,103,15)(4,221,104,16)(5,222,105,17)(6,223,106,18)(7,224,107,19)(8,211,108,20)(9,212,109,21)(10,213,110,22)(11,214,111,23)(12,215,112,24)(13,216,99,25)(14,217,100,26)(29,150,139,198)(30,151,140,199)(31,152,127,200)(32,153,128,201)(33,154,129,202)(34,141,130,203)(35,142,131,204)(36,143,132,205)(37,144,133,206)(38,145,134,207)(39,146,135,208)(40,147,136,209)(41,148,137,210)(42,149,138,197)(43,61,50,68)(44,62,51,69)(45,63,52,70)(46,64,53,57)(47,65,54,58)(48,66,55,59)(49,67,56,60)(71,122,78,115)(72,123,79,116)(73,124,80,117)(74,125,81,118)(75,126,82,119)(76,113,83,120)(77,114,84,121)(85,180,92,173)(86,181,93,174)(87,182,94,175)(88,169,95,176)(89,170,96,177)(90,171,97,178)(91,172,98,179)(155,193,162,186)(156,194,163,187)(157,195,164,188)(158,196,165,189)(159,183,166,190)(160,184,167,191)(161,185,168,192), (1,124,108,93)(2,94,109,125)(3,126,110,95)(4,96,111,113)(5,114,112,97)(6,98,99,115)(7,116,100,85)(8,86,101,117)(9,118,102,87)(10,88,103,119)(11,120,104,89)(12,90,105,121)(13,122,106,91)(14,92,107,123)(15,82,213,176)(16,177,214,83)(17,84,215,178)(18,179,216,71)(19,72,217,180)(20,181,218,73)(21,74,219,182)(22,169,220,75)(23,76,221,170)(24,171,222,77)(25,78,223,172)(26,173,224,79)(27,80,211,174)(28,175,212,81)(29,187,132,57)(30,58,133,188)(31,189,134,59)(32,60,135,190)(33,191,136,61)(34,62,137,192)(35,193,138,63)(36,64,139,194)(37,195,140,65)(38,66,127,196)(39,183,128,67)(40,68,129,184)(41,185,130,69)(42,70,131,186)(43,154,167,209)(44,210,168,141)(45,142,155,197)(46,198,156,143)(47,144,157,199)(48,200,158,145)(49,146,159,201)(50,202,160,147)(51,148,161,203)(52,204,162,149)(53,150,163,205)(54,206,164,151)(55,152,165,207)(56,208,166,153), (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), (1,139,8,132)(2,138,9,131)(3,137,10,130)(4,136,11,129)(5,135,12,128)(6,134,13,127)(7,133,14,140)(15,148,22,141)(16,147,23,154)(17,146,24,153)(18,145,25,152)(19,144,26,151)(20,143,27,150)(21,142,28,149)(29,108,36,101)(30,107,37,100)(31,106,38,99)(32,105,39,112)(33,104,40,111)(34,103,41,110)(35,102,42,109)(43,177,160,76)(44,176,161,75)(45,175,162,74)(46,174,163,73)(47,173,164,72)(48,172,165,71)(49,171,166,84)(50,170,167,83)(51,169,168,82)(52,182,155,81)(53,181,156,80)(54,180,157,79)(55,179,158,78)(56,178,159,77)(57,93,194,117)(58,92,195,116)(59,91,196,115)(60,90,183,114)(61,89,184,113)(62,88,185,126)(63,87,186,125)(64,86,187,124)(65,85,188,123)(66,98,189,122)(67,97,190,121)(68,96,191,120)(69,95,192,119)(70,94,193,118)(197,212,204,219)(198,211,205,218)(199,224,206,217)(200,223,207,216)(201,222,208,215)(202,221,209,214)(203,220,210,213)>;
G:=Group( (1,218,101,27)(2,219,102,28)(3,220,103,15)(4,221,104,16)(5,222,105,17)(6,223,106,18)(7,224,107,19)(8,211,108,20)(9,212,109,21)(10,213,110,22)(11,214,111,23)(12,215,112,24)(13,216,99,25)(14,217,100,26)(29,150,139,198)(30,151,140,199)(31,152,127,200)(32,153,128,201)(33,154,129,202)(34,141,130,203)(35,142,131,204)(36,143,132,205)(37,144,133,206)(38,145,134,207)(39,146,135,208)(40,147,136,209)(41,148,137,210)(42,149,138,197)(43,61,50,68)(44,62,51,69)(45,63,52,70)(46,64,53,57)(47,65,54,58)(48,66,55,59)(49,67,56,60)(71,122,78,115)(72,123,79,116)(73,124,80,117)(74,125,81,118)(75,126,82,119)(76,113,83,120)(77,114,84,121)(85,180,92,173)(86,181,93,174)(87,182,94,175)(88,169,95,176)(89,170,96,177)(90,171,97,178)(91,172,98,179)(155,193,162,186)(156,194,163,187)(157,195,164,188)(158,196,165,189)(159,183,166,190)(160,184,167,191)(161,185,168,192), (1,124,108,93)(2,94,109,125)(3,126,110,95)(4,96,111,113)(5,114,112,97)(6,98,99,115)(7,116,100,85)(8,86,101,117)(9,118,102,87)(10,88,103,119)(11,120,104,89)(12,90,105,121)(13,122,106,91)(14,92,107,123)(15,82,213,176)(16,177,214,83)(17,84,215,178)(18,179,216,71)(19,72,217,180)(20,181,218,73)(21,74,219,182)(22,169,220,75)(23,76,221,170)(24,171,222,77)(25,78,223,172)(26,173,224,79)(27,80,211,174)(28,175,212,81)(29,187,132,57)(30,58,133,188)(31,189,134,59)(32,60,135,190)(33,191,136,61)(34,62,137,192)(35,193,138,63)(36,64,139,194)(37,195,140,65)(38,66,127,196)(39,183,128,67)(40,68,129,184)(41,185,130,69)(42,70,131,186)(43,154,167,209)(44,210,168,141)(45,142,155,197)(46,198,156,143)(47,144,157,199)(48,200,158,145)(49,146,159,201)(50,202,160,147)(51,148,161,203)(52,204,162,149)(53,150,163,205)(54,206,164,151)(55,152,165,207)(56,208,166,153), (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), (1,139,8,132)(2,138,9,131)(3,137,10,130)(4,136,11,129)(5,135,12,128)(6,134,13,127)(7,133,14,140)(15,148,22,141)(16,147,23,154)(17,146,24,153)(18,145,25,152)(19,144,26,151)(20,143,27,150)(21,142,28,149)(29,108,36,101)(30,107,37,100)(31,106,38,99)(32,105,39,112)(33,104,40,111)(34,103,41,110)(35,102,42,109)(43,177,160,76)(44,176,161,75)(45,175,162,74)(46,174,163,73)(47,173,164,72)(48,172,165,71)(49,171,166,84)(50,170,167,83)(51,169,168,82)(52,182,155,81)(53,181,156,80)(54,180,157,79)(55,179,158,78)(56,178,159,77)(57,93,194,117)(58,92,195,116)(59,91,196,115)(60,90,183,114)(61,89,184,113)(62,88,185,126)(63,87,186,125)(64,86,187,124)(65,85,188,123)(66,98,189,122)(67,97,190,121)(68,96,191,120)(69,95,192,119)(70,94,193,118)(197,212,204,219)(198,211,205,218)(199,224,206,217)(200,223,207,216)(201,222,208,215)(202,221,209,214)(203,220,210,213) );
G=PermutationGroup([[(1,218,101,27),(2,219,102,28),(3,220,103,15),(4,221,104,16),(5,222,105,17),(6,223,106,18),(7,224,107,19),(8,211,108,20),(9,212,109,21),(10,213,110,22),(11,214,111,23),(12,215,112,24),(13,216,99,25),(14,217,100,26),(29,150,139,198),(30,151,140,199),(31,152,127,200),(32,153,128,201),(33,154,129,202),(34,141,130,203),(35,142,131,204),(36,143,132,205),(37,144,133,206),(38,145,134,207),(39,146,135,208),(40,147,136,209),(41,148,137,210),(42,149,138,197),(43,61,50,68),(44,62,51,69),(45,63,52,70),(46,64,53,57),(47,65,54,58),(48,66,55,59),(49,67,56,60),(71,122,78,115),(72,123,79,116),(73,124,80,117),(74,125,81,118),(75,126,82,119),(76,113,83,120),(77,114,84,121),(85,180,92,173),(86,181,93,174),(87,182,94,175),(88,169,95,176),(89,170,96,177),(90,171,97,178),(91,172,98,179),(155,193,162,186),(156,194,163,187),(157,195,164,188),(158,196,165,189),(159,183,166,190),(160,184,167,191),(161,185,168,192)], [(1,124,108,93),(2,94,109,125),(3,126,110,95),(4,96,111,113),(5,114,112,97),(6,98,99,115),(7,116,100,85),(8,86,101,117),(9,118,102,87),(10,88,103,119),(11,120,104,89),(12,90,105,121),(13,122,106,91),(14,92,107,123),(15,82,213,176),(16,177,214,83),(17,84,215,178),(18,179,216,71),(19,72,217,180),(20,181,218,73),(21,74,219,182),(22,169,220,75),(23,76,221,170),(24,171,222,77),(25,78,223,172),(26,173,224,79),(27,80,211,174),(28,175,212,81),(29,187,132,57),(30,58,133,188),(31,189,134,59),(32,60,135,190),(33,191,136,61),(34,62,137,192),(35,193,138,63),(36,64,139,194),(37,195,140,65),(38,66,127,196),(39,183,128,67),(40,68,129,184),(41,185,130,69),(42,70,131,186),(43,154,167,209),(44,210,168,141),(45,142,155,197),(46,198,156,143),(47,144,157,199),(48,200,158,145),(49,146,159,201),(50,202,160,147),(51,148,161,203),(52,204,162,149),(53,150,163,205),(54,206,164,151),(55,152,165,207),(56,208,166,153)], [(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)], [(1,139,8,132),(2,138,9,131),(3,137,10,130),(4,136,11,129),(5,135,12,128),(6,134,13,127),(7,133,14,140),(15,148,22,141),(16,147,23,154),(17,146,24,153),(18,145,25,152),(19,144,26,151),(20,143,27,150),(21,142,28,149),(29,108,36,101),(30,107,37,100),(31,106,38,99),(32,105,39,112),(33,104,40,111),(34,103,41,110),(35,102,42,109),(43,177,160,76),(44,176,161,75),(45,175,162,74),(46,174,163,73),(47,173,164,72),(48,172,165,71),(49,171,166,84),(50,170,167,83),(51,169,168,82),(52,182,155,81),(53,181,156,80),(54,180,157,79),(55,179,158,78),(56,178,159,77),(57,93,194,117),(58,92,195,116),(59,91,196,115),(60,90,183,114),(61,89,184,113),(62,88,185,126),(63,87,186,125),(64,86,187,124),(65,85,188,123),(66,98,189,122),(67,97,190,121),(68,96,191,120),(69,95,192,119),(70,94,193,118),(197,212,204,219),(198,211,205,218),(199,224,206,217),(200,223,207,216),(201,222,208,215),(202,221,209,214),(203,220,210,213)]])
70 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | ··· | 4P | 4Q | 4R | 4S | 4T | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28R |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 7 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
70 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | D4⋊2D7 | D4⋊2D7 | D7×C4○D4 |
| kernel | C4⋊C4.178D14 | C23.11D14 | C23.D14 | Dic7⋊3Q8 | C28.3Q8 | C2×C4×Dic7 | C28.48D4 | D4×Dic7 | C23.18D14 | C28.17D4 | C7×C4⋊D4 | C4⋊D4 | Dic7 | C28 | C2×C14 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 3 | 2 | 1 | 1 | 3 | 4 | 4 | 4 | 6 | 3 | 3 | 9 | 6 | 6 | 6 |
Matrix representation of C4⋊C4.178D14 ►in GL6(𝔽29)
| 8 | 6 | 0 | 0 | 0 | 0 |
| 23 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 23 | 21 | 0 | 0 | 0 | 0 |
| 8 | 6 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 10 | 0 | 0 |
| 0 | 0 | 9 | 9 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 8 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(6,GF(29))| [8,23,0,0,0,0,6,21,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[23,8,0,0,0,0,21,6,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,0,17,0,0,0,0,17,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,23,9,0,0,0,0,10,9,0,0,0,0,0,0,1,0,0,0,0,0,0,28],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,28,0,0,0,0,0,8,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1] >;
C4⋊C4.178D14 in GAP, Magma, Sage, TeX
C_4\rtimes C_4._{178}D_{14} % in TeX
G:=Group("C4:C4.178D14"); // GroupNames label
G:=SmallGroup(448,1053);
// by ID
G=gap.SmallGroup(448,1053);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,100,794,297,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b^2,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations