G = C14.232- 1+4 order 448 = 26·7
23rd non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C2×Q8=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.232- 1+4, C28⋊Q8⋊27C2, C22⋊Q8⋊18D7, C4⋊C4.196D14, (Q8×Dic7)⋊15C2, D14⋊3Q8⋊22C2, (C2×C28).62C23, (C2×Q8).131D14, C22⋊C4.21D14, Dic7⋊3Q8⋊29C2, C28.212(C4○D4), (C2×C14).185C24, (C22×C4).247D14, C4.101(D4⋊2D7), D14⋊C4.130C22, Dic7.37(C4○D4), C23.D14⋊25C2, Dic7⋊C4.33C22, C4⋊Dic7.376C22, Dic7.D4.2C2, (Q8×C14).115C22, (C22×D7).76C23, C22.206(C23×D7), C23.124(C22×D7), C23.21D14⋊30C2, (C22×C28).260C22, (C22×C14).213C23, C7⋊5(C22.50C24), (C4×Dic7).113C22, (C2×Dic7).239C23, C23.D7.124C22, C2.24(Q8.10D14), (C2×Dic14).163C22, C2.56(D7×C4○D4), C4⋊C4⋊7D7⋊29C2, C4⋊C4⋊D7⋊20C2, (C4×C7⋊D4).10C2, (C7×C22⋊Q8)⋊21C2, C14.168(C2×C4○D4), C2.48(C2×D4⋊2D7), (C2×C4×D7).102C22, (C2×C4).55(C22×D7), (C7×C4⋊C4).166C22, (C2×C7⋊D4).132C22, (C7×C22⋊C4).40C22, SmallGroup(448,1094)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.232- 1+4
G = < a,b,c,d,e | a14=b4=1, c2=a7, d2=a7b2, e2=b2, ab=ba, cac-1=dad-1=a-1, ae=ea, cbc-1=a7b-1, bd=db, be=eb, dcd-1=a7c, ce=ec, ede-1=b2d >
Subgroups: 828 in 212 conjugacy classes, 97 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22⋊Q8, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×Q8, C22×D7, C22×C14, C22.50C24, C4×Dic7, C4×Dic7, Dic7⋊C4, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D14⋊C4, C23.D7, C23.D7, C7×C22⋊C4, C7×C4⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C22×C28, Q8×C14, C23.D14, Dic7.D4, Dic7⋊3Q8, C28⋊Q8, C4⋊C4⋊7D7, C4⋊C4⋊D7, C23.21D14, C4×C7⋊D4, Q8×Dic7, D14⋊3Q8, C7×C22⋊Q8, C14.232- 1+4
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.50C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, Q8.10D14, D7×C4○D4, C14.232- 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)
(1 165 18 143)(2 166 19 144)(3 167 20 145)(4 168 21 146)(5 155 22 147)(6 156 23 148)(7 157 24 149)(8 158 25 150)(9 159 26 151)(10 160 27 152)(11 161 28 153)(12 162 15 154)(13 163 16 141)(14 164 17 142)(29 135 44 124)(30 136 45 125)(31 137 46 126)(32 138 47 113)(33 139 48 114)(34 140 49 115)(35 127 50 116)(36 128 51 117)(37 129 52 118)(38 130 53 119)(39 131 54 120)(40 132 55 121)(41 133 56 122)(42 134 43 123)(57 215 80 206)(58 216 81 207)(59 217 82 208)(60 218 83 209)(61 219 84 210)(62 220 71 197)(63 221 72 198)(64 222 73 199)(65 223 74 200)(66 224 75 201)(67 211 76 202)(68 212 77 203)(69 213 78 204)(70 214 79 205)(85 188 102 177)(86 189 103 178)(87 190 104 179)(88 191 105 180)(89 192 106 181)(90 193 107 182)(91 194 108 169)(92 195 109 170)(93 196 110 171)(94 183 111 172)(95 184 112 173)(96 185 99 174)(97 186 100 175)(98 187 101 176)
(1 143 8 150)(2 142 9 149)(3 141 10 148)(4 154 11 147)(5 153 12 146)(6 152 13 145)(7 151 14 144)(15 168 22 161)(16 167 23 160)(17 166 24 159)(18 165 25 158)(19 164 26 157)(20 163 27 156)(21 162 28 155)(29 128 36 135)(30 127 37 134)(31 140 38 133)(32 139 39 132)(33 138 40 131)(34 137 41 130)(35 136 42 129)(43 118 50 125)(44 117 51 124)(45 116 52 123)(46 115 53 122)(47 114 54 121)(48 113 55 120)(49 126 56 119)(57 199 64 206)(58 198 65 205)(59 197 66 204)(60 210 67 203)(61 209 68 202)(62 208 69 201)(63 207 70 200)(71 217 78 224)(72 216 79 223)(73 215 80 222)(74 214 81 221)(75 213 82 220)(76 212 83 219)(77 211 84 218)(85 190 92 183)(86 189 93 196)(87 188 94 195)(88 187 95 194)(89 186 96 193)(90 185 97 192)(91 184 98 191)(99 182 106 175)(100 181 107 174)(101 180 108 173)(102 179 109 172)(103 178 110 171)(104 177 111 170)(105 176 112 169)
(1 64 25 80)(2 63 26 79)(3 62 27 78)(4 61 28 77)(5 60 15 76)(6 59 16 75)(7 58 17 74)(8 57 18 73)(9 70 19 72)(10 69 20 71)(11 68 21 84)(12 67 22 83)(13 66 23 82)(14 65 24 81)(29 103 51 93)(30 102 52 92)(31 101 53 91)(32 100 54 90)(33 99 55 89)(34 112 56 88)(35 111 43 87)(36 110 44 86)(37 109 45 85)(38 108 46 98)(39 107 47 97)(40 106 48 96)(41 105 49 95)(42 104 50 94)(113 186 131 182)(114 185 132 181)(115 184 133 180)(116 183 134 179)(117 196 135 178)(118 195 136 177)(119 194 137 176)(120 193 138 175)(121 192 139 174)(122 191 140 173)(123 190 127 172)(124 189 128 171)(125 188 129 170)(126 187 130 169)(141 201 156 217)(142 200 157 216)(143 199 158 215)(144 198 159 214)(145 197 160 213)(146 210 161 212)(147 209 162 211)(148 208 163 224)(149 207 164 223)(150 206 165 222)(151 205 166 221)(152 204 167 220)(153 203 168 219)(154 202 155 218)
(1 128 18 117)(2 129 19 118)(3 130 20 119)(4 131 21 120)(5 132 22 121)(6 133 23 122)(7 134 24 123)(8 135 25 124)(9 136 26 125)(10 137 27 126)(11 138 28 113)(12 139 15 114)(13 140 16 115)(14 127 17 116)(29 158 44 150)(30 159 45 151)(31 160 46 152)(32 161 47 153)(33 162 48 154)(34 163 49 141)(35 164 50 142)(36 165 51 143)(37 166 52 144)(38 167 53 145)(39 168 54 146)(40 155 55 147)(41 156 56 148)(42 157 43 149)(57 189 80 178)(58 190 81 179)(59 191 82 180)(60 192 83 181)(61 193 84 182)(62 194 71 169)(63 195 72 170)(64 196 73 171)(65 183 74 172)(66 184 75 173)(67 185 76 174)(68 186 77 175)(69 187 78 176)(70 188 79 177)(85 214 102 205)(86 215 103 206)(87 216 104 207)(88 217 105 208)(89 218 106 209)(90 219 107 210)(91 220 108 197)(92 221 109 198)(93 222 110 199)(94 223 111 200)(95 224 112 201)(96 211 99 202)(97 212 100 203)(98 213 101 204)
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), (1,165,18,143)(2,166,19,144)(3,167,20,145)(4,168,21,146)(5,155,22,147)(6,156,23,148)(7,157,24,149)(8,158,25,150)(9,159,26,151)(10,160,27,152)(11,161,28,153)(12,162,15,154)(13,163,16,141)(14,164,17,142)(29,135,44,124)(30,136,45,125)(31,137,46,126)(32,138,47,113)(33,139,48,114)(34,140,49,115)(35,127,50,116)(36,128,51,117)(37,129,52,118)(38,130,53,119)(39,131,54,120)(40,132,55,121)(41,133,56,122)(42,134,43,123)(57,215,80,206)(58,216,81,207)(59,217,82,208)(60,218,83,209)(61,219,84,210)(62,220,71,197)(63,221,72,198)(64,222,73,199)(65,223,74,200)(66,224,75,201)(67,211,76,202)(68,212,77,203)(69,213,78,204)(70,214,79,205)(85,188,102,177)(86,189,103,178)(87,190,104,179)(88,191,105,180)(89,192,106,181)(90,193,107,182)(91,194,108,169)(92,195,109,170)(93,196,110,171)(94,183,111,172)(95,184,112,173)(96,185,99,174)(97,186,100,175)(98,187,101,176), (1,143,8,150)(2,142,9,149)(3,141,10,148)(4,154,11,147)(5,153,12,146)(6,152,13,145)(7,151,14,144)(15,168,22,161)(16,167,23,160)(17,166,24,159)(18,165,25,158)(19,164,26,157)(20,163,27,156)(21,162,28,155)(29,128,36,135)(30,127,37,134)(31,140,38,133)(32,139,39,132)(33,138,40,131)(34,137,41,130)(35,136,42,129)(43,118,50,125)(44,117,51,124)(45,116,52,123)(46,115,53,122)(47,114,54,121)(48,113,55,120)(49,126,56,119)(57,199,64,206)(58,198,65,205)(59,197,66,204)(60,210,67,203)(61,209,68,202)(62,208,69,201)(63,207,70,200)(71,217,78,224)(72,216,79,223)(73,215,80,222)(74,214,81,221)(75,213,82,220)(76,212,83,219)(77,211,84,218)(85,190,92,183)(86,189,93,196)(87,188,94,195)(88,187,95,194)(89,186,96,193)(90,185,97,192)(91,184,98,191)(99,182,106,175)(100,181,107,174)(101,180,108,173)(102,179,109,172)(103,178,110,171)(104,177,111,170)(105,176,112,169), (1,64,25,80)(2,63,26,79)(3,62,27,78)(4,61,28,77)(5,60,15,76)(6,59,16,75)(7,58,17,74)(8,57,18,73)(9,70,19,72)(10,69,20,71)(11,68,21,84)(12,67,22,83)(13,66,23,82)(14,65,24,81)(29,103,51,93)(30,102,52,92)(31,101,53,91)(32,100,54,90)(33,99,55,89)(34,112,56,88)(35,111,43,87)(36,110,44,86)(37,109,45,85)(38,108,46,98)(39,107,47,97)(40,106,48,96)(41,105,49,95)(42,104,50,94)(113,186,131,182)(114,185,132,181)(115,184,133,180)(116,183,134,179)(117,196,135,178)(118,195,136,177)(119,194,137,176)(120,193,138,175)(121,192,139,174)(122,191,140,173)(123,190,127,172)(124,189,128,171)(125,188,129,170)(126,187,130,169)(141,201,156,217)(142,200,157,216)(143,199,158,215)(144,198,159,214)(145,197,160,213)(146,210,161,212)(147,209,162,211)(148,208,163,224)(149,207,164,223)(150,206,165,222)(151,205,166,221)(152,204,167,220)(153,203,168,219)(154,202,155,218), (1,128,18,117)(2,129,19,118)(3,130,20,119)(4,131,21,120)(5,132,22,121)(6,133,23,122)(7,134,24,123)(8,135,25,124)(9,136,26,125)(10,137,27,126)(11,138,28,113)(12,139,15,114)(13,140,16,115)(14,127,17,116)(29,158,44,150)(30,159,45,151)(31,160,46,152)(32,161,47,153)(33,162,48,154)(34,163,49,141)(35,164,50,142)(36,165,51,143)(37,166,52,144)(38,167,53,145)(39,168,54,146)(40,155,55,147)(41,156,56,148)(42,157,43,149)(57,189,80,178)(58,190,81,179)(59,191,82,180)(60,192,83,181)(61,193,84,182)(62,194,71,169)(63,195,72,170)(64,196,73,171)(65,183,74,172)(66,184,75,173)(67,185,76,174)(68,186,77,175)(69,187,78,176)(70,188,79,177)(85,214,102,205)(86,215,103,206)(87,216,104,207)(88,217,105,208)(89,218,106,209)(90,219,107,210)(91,220,108,197)(92,221,109,198)(93,222,110,199)(94,223,111,200)(95,224,112,201)(96,211,99,202)(97,212,100,203)(98,213,101,204)>;
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), (1,165,18,143)(2,166,19,144)(3,167,20,145)(4,168,21,146)(5,155,22,147)(6,156,23,148)(7,157,24,149)(8,158,25,150)(9,159,26,151)(10,160,27,152)(11,161,28,153)(12,162,15,154)(13,163,16,141)(14,164,17,142)(29,135,44,124)(30,136,45,125)(31,137,46,126)(32,138,47,113)(33,139,48,114)(34,140,49,115)(35,127,50,116)(36,128,51,117)(37,129,52,118)(38,130,53,119)(39,131,54,120)(40,132,55,121)(41,133,56,122)(42,134,43,123)(57,215,80,206)(58,216,81,207)(59,217,82,208)(60,218,83,209)(61,219,84,210)(62,220,71,197)(63,221,72,198)(64,222,73,199)(65,223,74,200)(66,224,75,201)(67,211,76,202)(68,212,77,203)(69,213,78,204)(70,214,79,205)(85,188,102,177)(86,189,103,178)(87,190,104,179)(88,191,105,180)(89,192,106,181)(90,193,107,182)(91,194,108,169)(92,195,109,170)(93,196,110,171)(94,183,111,172)(95,184,112,173)(96,185,99,174)(97,186,100,175)(98,187,101,176), (1,143,8,150)(2,142,9,149)(3,141,10,148)(4,154,11,147)(5,153,12,146)(6,152,13,145)(7,151,14,144)(15,168,22,161)(16,167,23,160)(17,166,24,159)(18,165,25,158)(19,164,26,157)(20,163,27,156)(21,162,28,155)(29,128,36,135)(30,127,37,134)(31,140,38,133)(32,139,39,132)(33,138,40,131)(34,137,41,130)(35,136,42,129)(43,118,50,125)(44,117,51,124)(45,116,52,123)(46,115,53,122)(47,114,54,121)(48,113,55,120)(49,126,56,119)(57,199,64,206)(58,198,65,205)(59,197,66,204)(60,210,67,203)(61,209,68,202)(62,208,69,201)(63,207,70,200)(71,217,78,224)(72,216,79,223)(73,215,80,222)(74,214,81,221)(75,213,82,220)(76,212,83,219)(77,211,84,218)(85,190,92,183)(86,189,93,196)(87,188,94,195)(88,187,95,194)(89,186,96,193)(90,185,97,192)(91,184,98,191)(99,182,106,175)(100,181,107,174)(101,180,108,173)(102,179,109,172)(103,178,110,171)(104,177,111,170)(105,176,112,169), (1,64,25,80)(2,63,26,79)(3,62,27,78)(4,61,28,77)(5,60,15,76)(6,59,16,75)(7,58,17,74)(8,57,18,73)(9,70,19,72)(10,69,20,71)(11,68,21,84)(12,67,22,83)(13,66,23,82)(14,65,24,81)(29,103,51,93)(30,102,52,92)(31,101,53,91)(32,100,54,90)(33,99,55,89)(34,112,56,88)(35,111,43,87)(36,110,44,86)(37,109,45,85)(38,108,46,98)(39,107,47,97)(40,106,48,96)(41,105,49,95)(42,104,50,94)(113,186,131,182)(114,185,132,181)(115,184,133,180)(116,183,134,179)(117,196,135,178)(118,195,136,177)(119,194,137,176)(120,193,138,175)(121,192,139,174)(122,191,140,173)(123,190,127,172)(124,189,128,171)(125,188,129,170)(126,187,130,169)(141,201,156,217)(142,200,157,216)(143,199,158,215)(144,198,159,214)(145,197,160,213)(146,210,161,212)(147,209,162,211)(148,208,163,224)(149,207,164,223)(150,206,165,222)(151,205,166,221)(152,204,167,220)(153,203,168,219)(154,202,155,218), (1,128,18,117)(2,129,19,118)(3,130,20,119)(4,131,21,120)(5,132,22,121)(6,133,23,122)(7,134,24,123)(8,135,25,124)(9,136,26,125)(10,137,27,126)(11,138,28,113)(12,139,15,114)(13,140,16,115)(14,127,17,116)(29,158,44,150)(30,159,45,151)(31,160,46,152)(32,161,47,153)(33,162,48,154)(34,163,49,141)(35,164,50,142)(36,165,51,143)(37,166,52,144)(38,167,53,145)(39,168,54,146)(40,155,55,147)(41,156,56,148)(42,157,43,149)(57,189,80,178)(58,190,81,179)(59,191,82,180)(60,192,83,181)(61,193,84,182)(62,194,71,169)(63,195,72,170)(64,196,73,171)(65,183,74,172)(66,184,75,173)(67,185,76,174)(68,186,77,175)(69,187,78,176)(70,188,79,177)(85,214,102,205)(86,215,103,206)(87,216,104,207)(88,217,105,208)(89,218,106,209)(90,219,107,210)(91,220,108,197)(92,221,109,198)(93,222,110,199)(94,223,111,200)(95,224,112,201)(96,211,99,202)(97,212,100,203)(98,213,101,204) );
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)], [(1,165,18,143),(2,166,19,144),(3,167,20,145),(4,168,21,146),(5,155,22,147),(6,156,23,148),(7,157,24,149),(8,158,25,150),(9,159,26,151),(10,160,27,152),(11,161,28,153),(12,162,15,154),(13,163,16,141),(14,164,17,142),(29,135,44,124),(30,136,45,125),(31,137,46,126),(32,138,47,113),(33,139,48,114),(34,140,49,115),(35,127,50,116),(36,128,51,117),(37,129,52,118),(38,130,53,119),(39,131,54,120),(40,132,55,121),(41,133,56,122),(42,134,43,123),(57,215,80,206),(58,216,81,207),(59,217,82,208),(60,218,83,209),(61,219,84,210),(62,220,71,197),(63,221,72,198),(64,222,73,199),(65,223,74,200),(66,224,75,201),(67,211,76,202),(68,212,77,203),(69,213,78,204),(70,214,79,205),(85,188,102,177),(86,189,103,178),(87,190,104,179),(88,191,105,180),(89,192,106,181),(90,193,107,182),(91,194,108,169),(92,195,109,170),(93,196,110,171),(94,183,111,172),(95,184,112,173),(96,185,99,174),(97,186,100,175),(98,187,101,176)], [(1,143,8,150),(2,142,9,149),(3,141,10,148),(4,154,11,147),(5,153,12,146),(6,152,13,145),(7,151,14,144),(15,168,22,161),(16,167,23,160),(17,166,24,159),(18,165,25,158),(19,164,26,157),(20,163,27,156),(21,162,28,155),(29,128,36,135),(30,127,37,134),(31,140,38,133),(32,139,39,132),(33,138,40,131),(34,137,41,130),(35,136,42,129),(43,118,50,125),(44,117,51,124),(45,116,52,123),(46,115,53,122),(47,114,54,121),(48,113,55,120),(49,126,56,119),(57,199,64,206),(58,198,65,205),(59,197,66,204),(60,210,67,203),(61,209,68,202),(62,208,69,201),(63,207,70,200),(71,217,78,224),(72,216,79,223),(73,215,80,222),(74,214,81,221),(75,213,82,220),(76,212,83,219),(77,211,84,218),(85,190,92,183),(86,189,93,196),(87,188,94,195),(88,187,95,194),(89,186,96,193),(90,185,97,192),(91,184,98,191),(99,182,106,175),(100,181,107,174),(101,180,108,173),(102,179,109,172),(103,178,110,171),(104,177,111,170),(105,176,112,169)], [(1,64,25,80),(2,63,26,79),(3,62,27,78),(4,61,28,77),(5,60,15,76),(6,59,16,75),(7,58,17,74),(8,57,18,73),(9,70,19,72),(10,69,20,71),(11,68,21,84),(12,67,22,83),(13,66,23,82),(14,65,24,81),(29,103,51,93),(30,102,52,92),(31,101,53,91),(32,100,54,90),(33,99,55,89),(34,112,56,88),(35,111,43,87),(36,110,44,86),(37,109,45,85),(38,108,46,98),(39,107,47,97),(40,106,48,96),(41,105,49,95),(42,104,50,94),(113,186,131,182),(114,185,132,181),(115,184,133,180),(116,183,134,179),(117,196,135,178),(118,195,136,177),(119,194,137,176),(120,193,138,175),(121,192,139,174),(122,191,140,173),(123,190,127,172),(124,189,128,171),(125,188,129,170),(126,187,130,169),(141,201,156,217),(142,200,157,216),(143,199,158,215),(144,198,159,214),(145,197,160,213),(146,210,161,212),(147,209,162,211),(148,208,163,224),(149,207,164,223),(150,206,165,222),(151,205,166,221),(152,204,167,220),(153,203,168,219),(154,202,155,218)], [(1,128,18,117),(2,129,19,118),(3,130,20,119),(4,131,21,120),(5,132,22,121),(6,133,23,122),(7,134,24,123),(8,135,25,124),(9,136,26,125),(10,137,27,126),(11,138,28,113),(12,139,15,114),(13,140,16,115),(14,127,17,116),(29,158,44,150),(30,159,45,151),(31,160,46,152),(32,161,47,153),(33,162,48,154),(34,163,49,141),(35,164,50,142),(36,165,51,143),(37,166,52,144),(38,167,53,145),(39,168,54,146),(40,155,55,147),(41,156,56,148),(42,157,43,149),(57,189,80,178),(58,190,81,179),(59,191,82,180),(60,192,83,181),(61,193,84,182),(62,194,71,169),(63,195,72,170),(64,196,73,171),(65,183,74,172),(66,184,75,173),(67,185,76,174),(68,186,77,175),(69,187,78,176),(70,188,79,177),(85,214,102,205),(86,215,103,206),(87,216,104,207),(88,217,105,208),(89,218,106,209),(90,219,107,210),(91,220,108,197),(92,221,109,198),(93,222,110,199),(94,223,111,200),(95,224,112,201),(96,211,99,202),(97,212,100,203),(98,213,101,204)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | ··· | 4P | 4Q | 4R | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28X |
| 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 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 8 | ··· | 8 |
67 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 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | C4○D4 | D14 | D14 | D14 | D14 | 2- 1+4 | D4⋊2D7 | Q8.10D14 | D7×C4○D4 |
| kernel | C14.232- 1+4 | C23.D14 | Dic7.D4 | Dic7⋊3Q8 | C28⋊Q8 | C4⋊C4⋊7D7 | C4⋊C4⋊D7 | C23.21D14 | C4×C7⋊D4 | Q8×Dic7 | D14⋊3Q8 | C7×C22⋊Q8 | C22⋊Q8 | Dic7 | C28 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×Q8 | C14 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 9 | 3 | 3 | 1 | 6 | 6 | 6 |
Matrix representation of C14.232- 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 0 | 0 |
| 0 | 0 | 4 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 7 | 25 | 0 | 0 | 0 | 0 |
| 12 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 7 | 20 | 0 | 0 | 0 | 0 |
| 12 | 22 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 11 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 3 | 19 | 0 | 0 | 0 | 0 |
| 1 | 26 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 18 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,25,4,0,0,0,0,25,11,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[7,12,0,0,0,0,25,22,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[7,12,0,0,0,0,20,22,0,0,0,0,0,0,28,11,0,0,0,0,0,1,0,0,0,0,0,0,17,0,0,0,0,0,0,12],[3,1,0,0,0,0,19,26,0,0,0,0,0,0,1,18,0,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,28,0],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,12] >;
C14.232- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{23}2_-^{1+4} % in TeX
G:=Group("C14.23ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1094);
// by ID
G=gap.SmallGroup(448,1094);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,100,1571,297,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=1,c^2=a^7,d^2=a^7*b^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=a^7*b^-1,b*d=d*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