G = C14.152- 1+4 order 448 = 26·7
15th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.152- 1+4, C4⋊C4.188D14, C22⋊Q8.9D7, (Q8×Dic7)⋊12C2, Dic7.Q8⋊17C2, (C2×C28).50C23, (C2×Q8).123D14, C22⋊C4.13D14, C28.3Q8⋊23C2, Dic7⋊3Q8⋊24C2, Dic7⋊Q8⋊13C2, C28.209(C4○D4), C4.72(D4⋊2D7), (C2×C14).169C24, (C22×C4).233D14, C28.48D4.16C2, Dic7⋊C4.24C22, C4⋊Dic7.311C22, (Q8×C14).104C22, (C2×Dic7).84C23, C23.D14.2C2, C22.190(C23×D7), C23.116(C22×D7), (C22×C28).249C22, (C22×C14).197C23, C7⋊3(C22.35C24), (C4×Dic7).103C22, C23.D7.114C22, C2.34(D4.10D14), C2.16(Q8.10D14), (C2×Dic14).159C22, C23.21D14.24C2, C14.89(C2×C4○D4), (C7×C22⋊Q8).9C2, C2.45(C2×D4⋊2D7), (C7×C4⋊C4).155C22, (C2×C4).182(C22×D7), (C7×C22⋊C4).24C22, SmallGroup(448,1078)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.152- 1+4
G = < a,b,c,d,e | a14=b4=1, c2=a7, d2=e2=b2, ab=ba, cac-1=dad-1=a-1, ae=ea, cbc-1=b-1, dbd-1=a7b, be=eb, dcd-1=a7c, ce=ec, ede-1=b2d >
Subgroups: 668 in 192 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, Q8, C23, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×Q8, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C42⋊C2, C4×Q8, C22⋊Q8, C22⋊Q8, C42.C2, C42⋊2C2, C4⋊Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×Q8, C22×C14, C22.35C24, C4×Dic7, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C22×C28, Q8×C14, C23.D14, Dic7⋊3Q8, Dic7.Q8, C28.3Q8, C28.3Q8, C28.48D4, C23.21D14, Dic7⋊Q8, Q8×Dic7, C7×C22⋊Q8, C14.152- 1+4
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.35C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, Q8.10D14, D4.10D14, C14.152- 1+4
►On 224 points
Generators in S224
(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 73 27 70)(2 74 28 57)(3 75 15 58)(4 76 16 59)(5 77 17 60)(6 78 18 61)(7 79 19 62)(8 80 20 63)(9 81 21 64)(10 82 22 65)(11 83 23 66)(12 84 24 67)(13 71 25 68)(14 72 26 69)(29 110 46 94)(30 111 47 95)(31 112 48 96)(32 99 49 97)(33 100 50 98)(34 101 51 85)(35 102 52 86)(36 103 53 87)(37 104 54 88)(38 105 55 89)(39 106 56 90)(40 107 43 91)(41 108 44 92)(42 109 45 93)(113 177 130 191)(114 178 131 192)(115 179 132 193)(116 180 133 194)(117 181 134 195)(118 182 135 196)(119 169 136 183)(120 170 137 184)(121 171 138 185)(122 172 139 186)(123 173 140 187)(124 174 127 188)(125 175 128 189)(126 176 129 190)(141 201 159 214)(142 202 160 215)(143 203 161 216)(144 204 162 217)(145 205 163 218)(146 206 164 219)(147 207 165 220)(148 208 166 221)(149 209 167 222)(150 210 168 223)(151 197 155 224)(152 198 156 211)(153 199 157 212)(154 200 158 213)
(1 186 8 193)(2 185 9 192)(3 184 10 191)(4 183 11 190)(5 196 12 189)(6 195 13 188)(7 194 14 187)(15 170 22 177)(16 169 23 176)(17 182 24 175)(18 181 25 174)(19 180 26 173)(20 179 27 172)(21 178 28 171)(29 218 36 211)(30 217 37 224)(31 216 38 223)(32 215 39 222)(33 214 40 221)(34 213 41 220)(35 212 42 219)(43 208 50 201)(44 207 51 200)(45 206 52 199)(46 205 53 198)(47 204 54 197)(48 203 55 210)(49 202 56 209)(57 121 64 114)(58 120 65 113)(59 119 66 126)(60 118 67 125)(61 117 68 124)(62 116 69 123)(63 115 70 122)(71 127 78 134)(72 140 79 133)(73 139 80 132)(74 138 81 131)(75 137 82 130)(76 136 83 129)(77 135 84 128)(85 154 92 147)(86 153 93 146)(87 152 94 145)(88 151 95 144)(89 150 96 143)(90 149 97 142)(91 148 98 141)(99 160 106 167)(100 159 107 166)(101 158 108 165)(102 157 109 164)(103 156 110 163)(104 155 111 162)(105 168 112 161)
(1 150 27 168)(2 149 28 167)(3 148 15 166)(4 147 16 165)(5 146 17 164)(6 145 18 163)(7 144 19 162)(8 143 20 161)(9 142 21 160)(10 141 22 159)(11 154 23 158)(12 153 24 157)(13 152 25 156)(14 151 26 155)(29 127 46 124)(30 140 47 123)(31 139 48 122)(32 138 49 121)(33 137 50 120)(34 136 51 119)(35 135 52 118)(36 134 53 117)(37 133 54 116)(38 132 55 115)(39 131 56 114)(40 130 43 113)(41 129 44 126)(42 128 45 125)(57 215 74 202)(58 214 75 201)(59 213 76 200)(60 212 77 199)(61 211 78 198)(62 224 79 197)(63 223 80 210)(64 222 81 209)(65 221 82 208)(66 220 83 207)(67 219 84 206)(68 218 71 205)(69 217 72 204)(70 216 73 203)(85 176 101 190)(86 175 102 189)(87 174 103 188)(88 173 104 187)(89 172 105 186)(90 171 106 185)(91 170 107 184)(92 169 108 183)(93 182 109 196)(94 181 110 195)(95 180 111 194)(96 179 112 193)(97 178 99 192)(98 177 100 191)
(1 80 27 63)(2 81 28 64)(3 82 15 65)(4 83 16 66)(5 84 17 67)(6 71 18 68)(7 72 19 69)(8 73 20 70)(9 74 21 57)(10 75 22 58)(11 76 23 59)(12 77 24 60)(13 78 25 61)(14 79 26 62)(29 110 46 94)(30 111 47 95)(31 112 48 96)(32 99 49 97)(33 100 50 98)(34 101 51 85)(35 102 52 86)(36 103 53 87)(37 104 54 88)(38 105 55 89)(39 106 56 90)(40 107 43 91)(41 108 44 92)(42 109 45 93)(113 184 130 170)(114 185 131 171)(115 186 132 172)(116 187 133 173)(117 188 134 174)(118 189 135 175)(119 190 136 176)(120 191 137 177)(121 192 138 178)(122 193 139 179)(123 194 140 180)(124 195 127 181)(125 196 128 182)(126 183 129 169)(141 214 159 201)(142 215 160 202)(143 216 161 203)(144 217 162 204)(145 218 163 205)(146 219 164 206)(147 220 165 207)(148 221 166 208)(149 222 167 209)(150 223 168 210)(151 224 155 197)(152 211 156 198)(153 212 157 199)(154 213 158 200)
G:=sub<Sym(224)| (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), (1,73,27,70)(2,74,28,57)(3,75,15,58)(4,76,16,59)(5,77,17,60)(6,78,18,61)(7,79,19,62)(8,80,20,63)(9,81,21,64)(10,82,22,65)(11,83,23,66)(12,84,24,67)(13,71,25,68)(14,72,26,69)(29,110,46,94)(30,111,47,95)(31,112,48,96)(32,99,49,97)(33,100,50,98)(34,101,51,85)(35,102,52,86)(36,103,53,87)(37,104,54,88)(38,105,55,89)(39,106,56,90)(40,107,43,91)(41,108,44,92)(42,109,45,93)(113,177,130,191)(114,178,131,192)(115,179,132,193)(116,180,133,194)(117,181,134,195)(118,182,135,196)(119,169,136,183)(120,170,137,184)(121,171,138,185)(122,172,139,186)(123,173,140,187)(124,174,127,188)(125,175,128,189)(126,176,129,190)(141,201,159,214)(142,202,160,215)(143,203,161,216)(144,204,162,217)(145,205,163,218)(146,206,164,219)(147,207,165,220)(148,208,166,221)(149,209,167,222)(150,210,168,223)(151,197,155,224)(152,198,156,211)(153,199,157,212)(154,200,158,213), (1,186,8,193)(2,185,9,192)(3,184,10,191)(4,183,11,190)(5,196,12,189)(6,195,13,188)(7,194,14,187)(15,170,22,177)(16,169,23,176)(17,182,24,175)(18,181,25,174)(19,180,26,173)(20,179,27,172)(21,178,28,171)(29,218,36,211)(30,217,37,224)(31,216,38,223)(32,215,39,222)(33,214,40,221)(34,213,41,220)(35,212,42,219)(43,208,50,201)(44,207,51,200)(45,206,52,199)(46,205,53,198)(47,204,54,197)(48,203,55,210)(49,202,56,209)(57,121,64,114)(58,120,65,113)(59,119,66,126)(60,118,67,125)(61,117,68,124)(62,116,69,123)(63,115,70,122)(71,127,78,134)(72,140,79,133)(73,139,80,132)(74,138,81,131)(75,137,82,130)(76,136,83,129)(77,135,84,128)(85,154,92,147)(86,153,93,146)(87,152,94,145)(88,151,95,144)(89,150,96,143)(90,149,97,142)(91,148,98,141)(99,160,106,167)(100,159,107,166)(101,158,108,165)(102,157,109,164)(103,156,110,163)(104,155,111,162)(105,168,112,161), (1,150,27,168)(2,149,28,167)(3,148,15,166)(4,147,16,165)(5,146,17,164)(6,145,18,163)(7,144,19,162)(8,143,20,161)(9,142,21,160)(10,141,22,159)(11,154,23,158)(12,153,24,157)(13,152,25,156)(14,151,26,155)(29,127,46,124)(30,140,47,123)(31,139,48,122)(32,138,49,121)(33,137,50,120)(34,136,51,119)(35,135,52,118)(36,134,53,117)(37,133,54,116)(38,132,55,115)(39,131,56,114)(40,130,43,113)(41,129,44,126)(42,128,45,125)(57,215,74,202)(58,214,75,201)(59,213,76,200)(60,212,77,199)(61,211,78,198)(62,224,79,197)(63,223,80,210)(64,222,81,209)(65,221,82,208)(66,220,83,207)(67,219,84,206)(68,218,71,205)(69,217,72,204)(70,216,73,203)(85,176,101,190)(86,175,102,189)(87,174,103,188)(88,173,104,187)(89,172,105,186)(90,171,106,185)(91,170,107,184)(92,169,108,183)(93,182,109,196)(94,181,110,195)(95,180,111,194)(96,179,112,193)(97,178,99,192)(98,177,100,191), (1,80,27,63)(2,81,28,64)(3,82,15,65)(4,83,16,66)(5,84,17,67)(6,71,18,68)(7,72,19,69)(8,73,20,70)(9,74,21,57)(10,75,22,58)(11,76,23,59)(12,77,24,60)(13,78,25,61)(14,79,26,62)(29,110,46,94)(30,111,47,95)(31,112,48,96)(32,99,49,97)(33,100,50,98)(34,101,51,85)(35,102,52,86)(36,103,53,87)(37,104,54,88)(38,105,55,89)(39,106,56,90)(40,107,43,91)(41,108,44,92)(42,109,45,93)(113,184,130,170)(114,185,131,171)(115,186,132,172)(116,187,133,173)(117,188,134,174)(118,189,135,175)(119,190,136,176)(120,191,137,177)(121,192,138,178)(122,193,139,179)(123,194,140,180)(124,195,127,181)(125,196,128,182)(126,183,129,169)(141,214,159,201)(142,215,160,202)(143,216,161,203)(144,217,162,204)(145,218,163,205)(146,219,164,206)(147,220,165,207)(148,221,166,208)(149,222,167,209)(150,223,168,210)(151,224,155,197)(152,211,156,198)(153,212,157,199)(154,213,158,200)>;
G:=Group( (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), (1,73,27,70)(2,74,28,57)(3,75,15,58)(4,76,16,59)(5,77,17,60)(6,78,18,61)(7,79,19,62)(8,80,20,63)(9,81,21,64)(10,82,22,65)(11,83,23,66)(12,84,24,67)(13,71,25,68)(14,72,26,69)(29,110,46,94)(30,111,47,95)(31,112,48,96)(32,99,49,97)(33,100,50,98)(34,101,51,85)(35,102,52,86)(36,103,53,87)(37,104,54,88)(38,105,55,89)(39,106,56,90)(40,107,43,91)(41,108,44,92)(42,109,45,93)(113,177,130,191)(114,178,131,192)(115,179,132,193)(116,180,133,194)(117,181,134,195)(118,182,135,196)(119,169,136,183)(120,170,137,184)(121,171,138,185)(122,172,139,186)(123,173,140,187)(124,174,127,188)(125,175,128,189)(126,176,129,190)(141,201,159,214)(142,202,160,215)(143,203,161,216)(144,204,162,217)(145,205,163,218)(146,206,164,219)(147,207,165,220)(148,208,166,221)(149,209,167,222)(150,210,168,223)(151,197,155,224)(152,198,156,211)(153,199,157,212)(154,200,158,213), (1,186,8,193)(2,185,9,192)(3,184,10,191)(4,183,11,190)(5,196,12,189)(6,195,13,188)(7,194,14,187)(15,170,22,177)(16,169,23,176)(17,182,24,175)(18,181,25,174)(19,180,26,173)(20,179,27,172)(21,178,28,171)(29,218,36,211)(30,217,37,224)(31,216,38,223)(32,215,39,222)(33,214,40,221)(34,213,41,220)(35,212,42,219)(43,208,50,201)(44,207,51,200)(45,206,52,199)(46,205,53,198)(47,204,54,197)(48,203,55,210)(49,202,56,209)(57,121,64,114)(58,120,65,113)(59,119,66,126)(60,118,67,125)(61,117,68,124)(62,116,69,123)(63,115,70,122)(71,127,78,134)(72,140,79,133)(73,139,80,132)(74,138,81,131)(75,137,82,130)(76,136,83,129)(77,135,84,128)(85,154,92,147)(86,153,93,146)(87,152,94,145)(88,151,95,144)(89,150,96,143)(90,149,97,142)(91,148,98,141)(99,160,106,167)(100,159,107,166)(101,158,108,165)(102,157,109,164)(103,156,110,163)(104,155,111,162)(105,168,112,161), (1,150,27,168)(2,149,28,167)(3,148,15,166)(4,147,16,165)(5,146,17,164)(6,145,18,163)(7,144,19,162)(8,143,20,161)(9,142,21,160)(10,141,22,159)(11,154,23,158)(12,153,24,157)(13,152,25,156)(14,151,26,155)(29,127,46,124)(30,140,47,123)(31,139,48,122)(32,138,49,121)(33,137,50,120)(34,136,51,119)(35,135,52,118)(36,134,53,117)(37,133,54,116)(38,132,55,115)(39,131,56,114)(40,130,43,113)(41,129,44,126)(42,128,45,125)(57,215,74,202)(58,214,75,201)(59,213,76,200)(60,212,77,199)(61,211,78,198)(62,224,79,197)(63,223,80,210)(64,222,81,209)(65,221,82,208)(66,220,83,207)(67,219,84,206)(68,218,71,205)(69,217,72,204)(70,216,73,203)(85,176,101,190)(86,175,102,189)(87,174,103,188)(88,173,104,187)(89,172,105,186)(90,171,106,185)(91,170,107,184)(92,169,108,183)(93,182,109,196)(94,181,110,195)(95,180,111,194)(96,179,112,193)(97,178,99,192)(98,177,100,191), (1,80,27,63)(2,81,28,64)(3,82,15,65)(4,83,16,66)(5,84,17,67)(6,71,18,68)(7,72,19,69)(8,73,20,70)(9,74,21,57)(10,75,22,58)(11,76,23,59)(12,77,24,60)(13,78,25,61)(14,79,26,62)(29,110,46,94)(30,111,47,95)(31,112,48,96)(32,99,49,97)(33,100,50,98)(34,101,51,85)(35,102,52,86)(36,103,53,87)(37,104,54,88)(38,105,55,89)(39,106,56,90)(40,107,43,91)(41,108,44,92)(42,109,45,93)(113,184,130,170)(114,185,131,171)(115,186,132,172)(116,187,133,173)(117,188,134,174)(118,189,135,175)(119,190,136,176)(120,191,137,177)(121,192,138,178)(122,193,139,179)(123,194,140,180)(124,195,127,181)(125,196,128,182)(126,183,129,169)(141,214,159,201)(142,215,160,202)(143,216,161,203)(144,217,162,204)(145,218,163,205)(146,219,164,206)(147,220,165,207)(148,221,166,208)(149,222,167,209)(150,223,168,210)(151,224,155,197)(152,211,156,198)(153,212,157,199)(154,213,158,200) );
G=PermutationGroup([[(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)], [(1,73,27,70),(2,74,28,57),(3,75,15,58),(4,76,16,59),(5,77,17,60),(6,78,18,61),(7,79,19,62),(8,80,20,63),(9,81,21,64),(10,82,22,65),(11,83,23,66),(12,84,24,67),(13,71,25,68),(14,72,26,69),(29,110,46,94),(30,111,47,95),(31,112,48,96),(32,99,49,97),(33,100,50,98),(34,101,51,85),(35,102,52,86),(36,103,53,87),(37,104,54,88),(38,105,55,89),(39,106,56,90),(40,107,43,91),(41,108,44,92),(42,109,45,93),(113,177,130,191),(114,178,131,192),(115,179,132,193),(116,180,133,194),(117,181,134,195),(118,182,135,196),(119,169,136,183),(120,170,137,184),(121,171,138,185),(122,172,139,186),(123,173,140,187),(124,174,127,188),(125,175,128,189),(126,176,129,190),(141,201,159,214),(142,202,160,215),(143,203,161,216),(144,204,162,217),(145,205,163,218),(146,206,164,219),(147,207,165,220),(148,208,166,221),(149,209,167,222),(150,210,168,223),(151,197,155,224),(152,198,156,211),(153,199,157,212),(154,200,158,213)], [(1,186,8,193),(2,185,9,192),(3,184,10,191),(4,183,11,190),(5,196,12,189),(6,195,13,188),(7,194,14,187),(15,170,22,177),(16,169,23,176),(17,182,24,175),(18,181,25,174),(19,180,26,173),(20,179,27,172),(21,178,28,171),(29,218,36,211),(30,217,37,224),(31,216,38,223),(32,215,39,222),(33,214,40,221),(34,213,41,220),(35,212,42,219),(43,208,50,201),(44,207,51,200),(45,206,52,199),(46,205,53,198),(47,204,54,197),(48,203,55,210),(49,202,56,209),(57,121,64,114),(58,120,65,113),(59,119,66,126),(60,118,67,125),(61,117,68,124),(62,116,69,123),(63,115,70,122),(71,127,78,134),(72,140,79,133),(73,139,80,132),(74,138,81,131),(75,137,82,130),(76,136,83,129),(77,135,84,128),(85,154,92,147),(86,153,93,146),(87,152,94,145),(88,151,95,144),(89,150,96,143),(90,149,97,142),(91,148,98,141),(99,160,106,167),(100,159,107,166),(101,158,108,165),(102,157,109,164),(103,156,110,163),(104,155,111,162),(105,168,112,161)], [(1,150,27,168),(2,149,28,167),(3,148,15,166),(4,147,16,165),(5,146,17,164),(6,145,18,163),(7,144,19,162),(8,143,20,161),(9,142,21,160),(10,141,22,159),(11,154,23,158),(12,153,24,157),(13,152,25,156),(14,151,26,155),(29,127,46,124),(30,140,47,123),(31,139,48,122),(32,138,49,121),(33,137,50,120),(34,136,51,119),(35,135,52,118),(36,134,53,117),(37,133,54,116),(38,132,55,115),(39,131,56,114),(40,130,43,113),(41,129,44,126),(42,128,45,125),(57,215,74,202),(58,214,75,201),(59,213,76,200),(60,212,77,199),(61,211,78,198),(62,224,79,197),(63,223,80,210),(64,222,81,209),(65,221,82,208),(66,220,83,207),(67,219,84,206),(68,218,71,205),(69,217,72,204),(70,216,73,203),(85,176,101,190),(86,175,102,189),(87,174,103,188),(88,173,104,187),(89,172,105,186),(90,171,106,185),(91,170,107,184),(92,169,108,183),(93,182,109,196),(94,181,110,195),(95,180,111,194),(96,179,112,193),(97,178,99,192),(98,177,100,191)], [(1,80,27,63),(2,81,28,64),(3,82,15,65),(4,83,16,66),(5,84,17,67),(6,71,18,68),(7,72,19,69),(8,73,20,70),(9,74,21,57),(10,75,22,58),(11,76,23,59),(12,77,24,60),(13,78,25,61),(14,79,26,62),(29,110,46,94),(30,111,47,95),(31,112,48,96),(32,99,49,97),(33,100,50,98),(34,101,51,85),(35,102,52,86),(36,103,53,87),(37,104,54,88),(38,105,55,89),(39,106,56,90),(40,107,43,91),(41,108,44,92),(42,109,45,93),(113,184,130,170),(114,185,131,171),(115,186,132,172),(116,187,133,173),(117,188,134,174),(118,189,135,175),(119,190,136,176),(120,191,137,177),(121,192,138,178),(122,193,139,179),(123,194,140,180),(124,195,127,181),(125,196,128,182),(126,183,129,169),(141,214,159,201),(142,215,160,202),(143,216,161,203),(144,217,162,204),(145,218,163,205),(146,219,164,206),(147,220,165,207),(148,221,166,208),(149,222,167,209),(150,223,168,210),(151,224,155,197),(152,211,156,198),(153,212,157,199),(154,213,158,200)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | ··· | 4G | 4H | 4I | 4J | 4K | 4L | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 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 | 2 | 2 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
64 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 | C2 | D7 | C4○D4 | D14 | D14 | D14 | D14 | 2- 1+4 | D4⋊2D7 | Q8.10D14 | D4.10D14 |
| kernel | C14.152- 1+4 | C23.D14 | Dic7⋊3Q8 | Dic7.Q8 | C28.3Q8 | C28.48D4 | C23.21D14 | Dic7⋊Q8 | Q8×Dic7 | C7×C22⋊Q8 | C22⋊Q8 | C28 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 4 | 1 | 2 | 3 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 6 | 9 | 3 | 3 | 2 | 6 | 6 | 6 |
Matrix representation of C14.152- 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 4 | 0 | 0 |
| 0 | 0 | 5 | 21 | 0 | 0 |
| 0 | 0 | 25 | 0 | 0 | 4 |
| 0 | 0 | 8 | 4 | 7 | 22 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 5 | 0 | 0 |
| 0 | 0 | 28 | 27 | 0 | 0 |
| 0 | 0 | 24 | 0 | 8 | 5 |
| 0 | 0 | 10 | 5 | 16 | 21 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 17 | 11 | 26 |
| 0 | 0 | 12 | 7 | 5 | 26 |
| 0 | 0 | 3 | 0 | 21 | 26 |
| 0 | 0 | 17 | 17 | 23 | 5 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 12 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 2 | 11 | 0 | 0 |
| 0 | 0 | 18 | 27 | 0 | 0 |
| 0 | 0 | 16 | 0 | 4 | 13 |
| 0 | 0 | 6 | 11 | 21 | 25 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 24 | 0 | 0 |
| 0 | 0 | 1 | 2 | 0 | 0 |
| 0 | 0 | 10 | 15 | 8 | 5 |
| 0 | 0 | 14 | 9 | 16 | 21 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,5,25,8,0,0,4,21,0,4,0,0,0,0,0,7,0,0,0,0,4,22],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,2,28,24,10,0,0,5,27,0,5,0,0,0,0,8,16,0,0,0,0,5,21],[12,0,0,0,0,0,0,17,0,0,0,0,0,0,25,12,3,17,0,0,17,7,0,17,0,0,11,5,21,23,0,0,26,26,26,5],[0,12,0,0,0,0,17,0,0,0,0,0,0,0,2,18,16,6,0,0,11,27,0,11,0,0,0,0,4,21,0,0,0,0,13,25],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,27,1,10,14,0,0,24,2,15,9,0,0,0,0,8,16,0,0,0,0,5,21] >;
C14.152- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{15}2_-^{1+4} % in TeX
G:=Group("C14.15ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1078);
// by ID
G=gap.SmallGroup(448,1078);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,120,219,268,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=1,c^2=a^7,d^2=e^2=b^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,a*e=e*a,c*b*c^-1=b^-1,d*b*d^-1=a^7*b,b*e=e*b,d*c*d^-1=a^7*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations