G = C14.792- 1+4 order 448 = 26·7
34th non-split extension by C14 of 2- 1+4 acting via 2- 1+4/C4○D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C14.792- 1+4, C28⋊Q8⋊30C2, C4⋊C4.103D14, Dic7.8(C2×D4), C22.42(D4×D7), D14⋊Q8⋊26C2, (C2×D4).158D14, (C2×C28).66C23, C22⋊C4.25D14, (C2×Dic7).79D4, C22.D4⋊2D7, C14.80(C22×D4), (C2×C14).192C24, D14⋊C4.30C22, (C22×C4).254D14, Dic7.D4⋊29C2, C22⋊Dic14⋊27C2, (C22×Dic14)⋊10C2, (D4×C14).130C22, C23.23D14⋊6C2, C22.D28⋊18C2, Dic7⋊C4.37C22, C4⋊Dic7.223C22, (C22×C28).85C22, (C22×C14).28C23, (C22×D7).83C23, C23.198(C22×D7), C22.213(C23×D7), C23.D7.38C22, C23.18D14⋊13C2, C23.11D14⋊10C2, C7⋊3(C23.38C23), (C4×Dic7).119C22, (C2×Dic7).242C23, C2.40(D4.10D14), (C2×Dic14).249C22, (C22×Dic7).126C22, C2.53(C2×D4×D7), (C2×C14).56(C2×D4), (C2×D4⋊2D7).8C2, (C2×C4×D7).108C22, (C7×C4⋊C4).172C22, (C7×C22.D4)⋊2C2, (C2×C4).188(C22×D7), (C2×C7⋊D4).44C22, (C7×C22⋊C4).47C22, SmallGroup(448,1101)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14.792- 1+4
G = < a,b,c,d,e | a14=b4=c2=1, d2=e2=b2, ab=ba, ac=ca, dad-1=a-1, ae=ea, cbc=b-1, bd=db, ebe-1=a7b, cd=dc, ce=ec, ede-1=b2d >
Subgroups: 1196 in 270 conjugacy classes, 103 normal (39 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C14, C42, C22⋊C4, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C42⋊C2, C22⋊Q8, C22.D4, C22.D4, C4.4D4, C4⋊Q8, C22×Q8, C2×C4○D4, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C23.38C23, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C23.D7, C7×C22⋊C4, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×Dic14, C2×C4×D7, D4⋊2D7, C22×Dic7, C2×C7⋊D4, C22×C28, D4×C14, C23.11D14, C22⋊Dic14, Dic7.D4, C22.D28, C28⋊Q8, D14⋊Q8, C23.23D14, C23.18D14, C7×C22.D4, C22×Dic14, C2×D4⋊2D7, C14.792- 1+4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C22×D4, 2- 1+4, C22×D7, C23.38C23, D4×D7, C23×D7, C2×D4×D7, D4.10D14, C14.792- 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 51 117 172)(2 52 118 173)(3 53 119 174)(4 54 120 175)(5 55 121 176)(6 56 122 177)(7 43 123 178)(8 44 124 179)(9 45 125 180)(10 46 126 181)(11 47 113 182)(12 48 114 169)(13 49 115 170)(14 50 116 171)(15 194 69 99)(16 195 70 100)(17 196 57 101)(18 183 58 102)(19 184 59 103)(20 185 60 104)(21 186 61 105)(22 187 62 106)(23 188 63 107)(24 189 64 108)(25 190 65 109)(26 191 66 110)(27 192 67 111)(28 193 68 112)(29 152 167 94)(30 153 168 95)(31 154 155 96)(32 141 156 97)(33 142 157 98)(34 143 158 85)(35 144 159 86)(36 145 160 87)(37 146 161 88)(38 147 162 89)(39 148 163 90)(40 149 164 91)(41 150 165 92)(42 151 166 93)(71 215 202 136)(72 216 203 137)(73 217 204 138)(74 218 205 139)(75 219 206 140)(76 220 207 127)(77 221 208 128)(78 222 209 129)(79 223 210 130)(80 224 197 131)(81 211 198 132)(82 212 199 133)(83 213 200 134)(84 214 201 135)
(15 69)(16 70)(17 57)(18 58)(19 59)(20 60)(21 61)(22 62)(23 63)(24 64)(25 65)(26 66)(27 67)(28 68)(29 167)(30 168)(31 155)(32 156)(33 157)(34 158)(35 159)(36 160)(37 161)(38 162)(39 163)(40 164)(41 165)(42 166)(43 178)(44 179)(45 180)(46 181)(47 182)(48 169)(49 170)(50 171)(51 172)(52 173)(53 174)(54 175)(55 176)(56 177)(71 202)(72 203)(73 204)(74 205)(75 206)(76 207)(77 208)(78 209)(79 210)(80 197)(81 198)(82 199)(83 200)(84 201)
(1 137 117 216)(2 136 118 215)(3 135 119 214)(4 134 120 213)(5 133 121 212)(6 132 122 211)(7 131 123 224)(8 130 124 223)(9 129 125 222)(10 128 126 221)(11 127 113 220)(12 140 114 219)(13 139 115 218)(14 138 116 217)(15 31 69 155)(16 30 70 168)(17 29 57 167)(18 42 58 166)(19 41 59 165)(20 40 60 164)(21 39 61 163)(22 38 62 162)(23 37 63 161)(24 36 64 160)(25 35 65 159)(26 34 66 158)(27 33 67 157)(28 32 68 156)(43 80 178 197)(44 79 179 210)(45 78 180 209)(46 77 181 208)(47 76 182 207)(48 75 169 206)(49 74 170 205)(50 73 171 204)(51 72 172 203)(52 71 173 202)(53 84 174 201)(54 83 175 200)(55 82 176 199)(56 81 177 198)(85 191 143 110)(86 190 144 109)(87 189 145 108)(88 188 146 107)(89 187 147 106)(90 186 148 105)(91 185 149 104)(92 184 150 103)(93 183 151 102)(94 196 152 101)(95 195 153 100)(96 194 154 99)(97 193 141 112)(98 192 142 111)
(1 187 117 106)(2 188 118 107)(3 189 119 108)(4 190 120 109)(5 191 121 110)(6 192 122 111)(7 193 123 112)(8 194 124 99)(9 195 125 100)(10 196 126 101)(11 183 113 102)(12 184 114 103)(13 185 115 104)(14 186 116 105)(15 51 69 172)(16 52 70 173)(17 53 57 174)(18 54 58 175)(19 55 59 176)(20 56 60 177)(21 43 61 178)(22 44 62 179)(23 45 63 180)(24 46 64 181)(25 47 65 182)(26 48 66 169)(27 49 67 170)(28 50 68 171)(29 201 167 84)(30 202 168 71)(31 203 155 72)(32 204 156 73)(33 205 157 74)(34 206 158 75)(35 207 159 76)(36 208 160 77)(37 209 161 78)(38 210 162 79)(39 197 163 80)(40 198 164 81)(41 199 165 82)(42 200 166 83)(85 212 143 133)(86 213 144 134)(87 214 145 135)(88 215 146 136)(89 216 147 137)(90 217 148 138)(91 218 149 139)(92 219 150 140)(93 220 151 127)(94 221 152 128)(95 222 153 129)(96 223 154 130)(97 224 141 131)(98 211 142 132)
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), (1,51,117,172)(2,52,118,173)(3,53,119,174)(4,54,120,175)(5,55,121,176)(6,56,122,177)(7,43,123,178)(8,44,124,179)(9,45,125,180)(10,46,126,181)(11,47,113,182)(12,48,114,169)(13,49,115,170)(14,50,116,171)(15,194,69,99)(16,195,70,100)(17,196,57,101)(18,183,58,102)(19,184,59,103)(20,185,60,104)(21,186,61,105)(22,187,62,106)(23,188,63,107)(24,189,64,108)(25,190,65,109)(26,191,66,110)(27,192,67,111)(28,193,68,112)(29,152,167,94)(30,153,168,95)(31,154,155,96)(32,141,156,97)(33,142,157,98)(34,143,158,85)(35,144,159,86)(36,145,160,87)(37,146,161,88)(38,147,162,89)(39,148,163,90)(40,149,164,91)(41,150,165,92)(42,151,166,93)(71,215,202,136)(72,216,203,137)(73,217,204,138)(74,218,205,139)(75,219,206,140)(76,220,207,127)(77,221,208,128)(78,222,209,129)(79,223,210,130)(80,224,197,131)(81,211,198,132)(82,212,199,133)(83,213,200,134)(84,214,201,135), (15,69)(16,70)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,167)(30,168)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,178)(44,179)(45,180)(46,181)(47,182)(48,169)(49,170)(50,171)(51,172)(52,173)(53,174)(54,175)(55,176)(56,177)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,197)(81,198)(82,199)(83,200)(84,201), (1,137,117,216)(2,136,118,215)(3,135,119,214)(4,134,120,213)(5,133,121,212)(6,132,122,211)(7,131,123,224)(8,130,124,223)(9,129,125,222)(10,128,126,221)(11,127,113,220)(12,140,114,219)(13,139,115,218)(14,138,116,217)(15,31,69,155)(16,30,70,168)(17,29,57,167)(18,42,58,166)(19,41,59,165)(20,40,60,164)(21,39,61,163)(22,38,62,162)(23,37,63,161)(24,36,64,160)(25,35,65,159)(26,34,66,158)(27,33,67,157)(28,32,68,156)(43,80,178,197)(44,79,179,210)(45,78,180,209)(46,77,181,208)(47,76,182,207)(48,75,169,206)(49,74,170,205)(50,73,171,204)(51,72,172,203)(52,71,173,202)(53,84,174,201)(54,83,175,200)(55,82,176,199)(56,81,177,198)(85,191,143,110)(86,190,144,109)(87,189,145,108)(88,188,146,107)(89,187,147,106)(90,186,148,105)(91,185,149,104)(92,184,150,103)(93,183,151,102)(94,196,152,101)(95,195,153,100)(96,194,154,99)(97,193,141,112)(98,192,142,111), (1,187,117,106)(2,188,118,107)(3,189,119,108)(4,190,120,109)(5,191,121,110)(6,192,122,111)(7,193,123,112)(8,194,124,99)(9,195,125,100)(10,196,126,101)(11,183,113,102)(12,184,114,103)(13,185,115,104)(14,186,116,105)(15,51,69,172)(16,52,70,173)(17,53,57,174)(18,54,58,175)(19,55,59,176)(20,56,60,177)(21,43,61,178)(22,44,62,179)(23,45,63,180)(24,46,64,181)(25,47,65,182)(26,48,66,169)(27,49,67,170)(28,50,68,171)(29,201,167,84)(30,202,168,71)(31,203,155,72)(32,204,156,73)(33,205,157,74)(34,206,158,75)(35,207,159,76)(36,208,160,77)(37,209,161,78)(38,210,162,79)(39,197,163,80)(40,198,164,81)(41,199,165,82)(42,200,166,83)(85,212,143,133)(86,213,144,134)(87,214,145,135)(88,215,146,136)(89,216,147,137)(90,217,148,138)(91,218,149,139)(92,219,150,140)(93,220,151,127)(94,221,152,128)(95,222,153,129)(96,223,154,130)(97,224,141,131)(98,211,142,132)>;
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), (1,51,117,172)(2,52,118,173)(3,53,119,174)(4,54,120,175)(5,55,121,176)(6,56,122,177)(7,43,123,178)(8,44,124,179)(9,45,125,180)(10,46,126,181)(11,47,113,182)(12,48,114,169)(13,49,115,170)(14,50,116,171)(15,194,69,99)(16,195,70,100)(17,196,57,101)(18,183,58,102)(19,184,59,103)(20,185,60,104)(21,186,61,105)(22,187,62,106)(23,188,63,107)(24,189,64,108)(25,190,65,109)(26,191,66,110)(27,192,67,111)(28,193,68,112)(29,152,167,94)(30,153,168,95)(31,154,155,96)(32,141,156,97)(33,142,157,98)(34,143,158,85)(35,144,159,86)(36,145,160,87)(37,146,161,88)(38,147,162,89)(39,148,163,90)(40,149,164,91)(41,150,165,92)(42,151,166,93)(71,215,202,136)(72,216,203,137)(73,217,204,138)(74,218,205,139)(75,219,206,140)(76,220,207,127)(77,221,208,128)(78,222,209,129)(79,223,210,130)(80,224,197,131)(81,211,198,132)(82,212,199,133)(83,213,200,134)(84,214,201,135), (15,69)(16,70)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,64)(25,65)(26,66)(27,67)(28,68)(29,167)(30,168)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,178)(44,179)(45,180)(46,181)(47,182)(48,169)(49,170)(50,171)(51,172)(52,173)(53,174)(54,175)(55,176)(56,177)(71,202)(72,203)(73,204)(74,205)(75,206)(76,207)(77,208)(78,209)(79,210)(80,197)(81,198)(82,199)(83,200)(84,201), (1,137,117,216)(2,136,118,215)(3,135,119,214)(4,134,120,213)(5,133,121,212)(6,132,122,211)(7,131,123,224)(8,130,124,223)(9,129,125,222)(10,128,126,221)(11,127,113,220)(12,140,114,219)(13,139,115,218)(14,138,116,217)(15,31,69,155)(16,30,70,168)(17,29,57,167)(18,42,58,166)(19,41,59,165)(20,40,60,164)(21,39,61,163)(22,38,62,162)(23,37,63,161)(24,36,64,160)(25,35,65,159)(26,34,66,158)(27,33,67,157)(28,32,68,156)(43,80,178,197)(44,79,179,210)(45,78,180,209)(46,77,181,208)(47,76,182,207)(48,75,169,206)(49,74,170,205)(50,73,171,204)(51,72,172,203)(52,71,173,202)(53,84,174,201)(54,83,175,200)(55,82,176,199)(56,81,177,198)(85,191,143,110)(86,190,144,109)(87,189,145,108)(88,188,146,107)(89,187,147,106)(90,186,148,105)(91,185,149,104)(92,184,150,103)(93,183,151,102)(94,196,152,101)(95,195,153,100)(96,194,154,99)(97,193,141,112)(98,192,142,111), (1,187,117,106)(2,188,118,107)(3,189,119,108)(4,190,120,109)(5,191,121,110)(6,192,122,111)(7,193,123,112)(8,194,124,99)(9,195,125,100)(10,196,126,101)(11,183,113,102)(12,184,114,103)(13,185,115,104)(14,186,116,105)(15,51,69,172)(16,52,70,173)(17,53,57,174)(18,54,58,175)(19,55,59,176)(20,56,60,177)(21,43,61,178)(22,44,62,179)(23,45,63,180)(24,46,64,181)(25,47,65,182)(26,48,66,169)(27,49,67,170)(28,50,68,171)(29,201,167,84)(30,202,168,71)(31,203,155,72)(32,204,156,73)(33,205,157,74)(34,206,158,75)(35,207,159,76)(36,208,160,77)(37,209,161,78)(38,210,162,79)(39,197,163,80)(40,198,164,81)(41,199,165,82)(42,200,166,83)(85,212,143,133)(86,213,144,134)(87,214,145,135)(88,215,146,136)(89,216,147,137)(90,217,148,138)(91,218,149,139)(92,219,150,140)(93,220,151,127)(94,221,152,128)(95,222,153,129)(96,223,154,130)(97,224,141,131)(98,211,142,132) );
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)], [(1,51,117,172),(2,52,118,173),(3,53,119,174),(4,54,120,175),(5,55,121,176),(6,56,122,177),(7,43,123,178),(8,44,124,179),(9,45,125,180),(10,46,126,181),(11,47,113,182),(12,48,114,169),(13,49,115,170),(14,50,116,171),(15,194,69,99),(16,195,70,100),(17,196,57,101),(18,183,58,102),(19,184,59,103),(20,185,60,104),(21,186,61,105),(22,187,62,106),(23,188,63,107),(24,189,64,108),(25,190,65,109),(26,191,66,110),(27,192,67,111),(28,193,68,112),(29,152,167,94),(30,153,168,95),(31,154,155,96),(32,141,156,97),(33,142,157,98),(34,143,158,85),(35,144,159,86),(36,145,160,87),(37,146,161,88),(38,147,162,89),(39,148,163,90),(40,149,164,91),(41,150,165,92),(42,151,166,93),(71,215,202,136),(72,216,203,137),(73,217,204,138),(74,218,205,139),(75,219,206,140),(76,220,207,127),(77,221,208,128),(78,222,209,129),(79,223,210,130),(80,224,197,131),(81,211,198,132),(82,212,199,133),(83,213,200,134),(84,214,201,135)], [(15,69),(16,70),(17,57),(18,58),(19,59),(20,60),(21,61),(22,62),(23,63),(24,64),(25,65),(26,66),(27,67),(28,68),(29,167),(30,168),(31,155),(32,156),(33,157),(34,158),(35,159),(36,160),(37,161),(38,162),(39,163),(40,164),(41,165),(42,166),(43,178),(44,179),(45,180),(46,181),(47,182),(48,169),(49,170),(50,171),(51,172),(52,173),(53,174),(54,175),(55,176),(56,177),(71,202),(72,203),(73,204),(74,205),(75,206),(76,207),(77,208),(78,209),(79,210),(80,197),(81,198),(82,199),(83,200),(84,201)], [(1,137,117,216),(2,136,118,215),(3,135,119,214),(4,134,120,213),(5,133,121,212),(6,132,122,211),(7,131,123,224),(8,130,124,223),(9,129,125,222),(10,128,126,221),(11,127,113,220),(12,140,114,219),(13,139,115,218),(14,138,116,217),(15,31,69,155),(16,30,70,168),(17,29,57,167),(18,42,58,166),(19,41,59,165),(20,40,60,164),(21,39,61,163),(22,38,62,162),(23,37,63,161),(24,36,64,160),(25,35,65,159),(26,34,66,158),(27,33,67,157),(28,32,68,156),(43,80,178,197),(44,79,179,210),(45,78,180,209),(46,77,181,208),(47,76,182,207),(48,75,169,206),(49,74,170,205),(50,73,171,204),(51,72,172,203),(52,71,173,202),(53,84,174,201),(54,83,175,200),(55,82,176,199),(56,81,177,198),(85,191,143,110),(86,190,144,109),(87,189,145,108),(88,188,146,107),(89,187,147,106),(90,186,148,105),(91,185,149,104),(92,184,150,103),(93,183,151,102),(94,196,152,101),(95,195,153,100),(96,194,154,99),(97,193,141,112),(98,192,142,111)], [(1,187,117,106),(2,188,118,107),(3,189,119,108),(4,190,120,109),(5,191,121,110),(6,192,122,111),(7,193,123,112),(8,194,124,99),(9,195,125,100),(10,196,126,101),(11,183,113,102),(12,184,114,103),(13,185,115,104),(14,186,116,105),(15,51,69,172),(16,52,70,173),(17,53,57,174),(18,54,58,175),(19,55,59,176),(20,56,60,177),(21,43,61,178),(22,44,62,179),(23,45,63,180),(24,46,64,181),(25,47,65,182),(26,48,66,169),(27,49,67,170),(28,50,68,171),(29,201,167,84),(30,202,168,71),(31,203,155,72),(32,204,156,73),(33,205,157,74),(34,206,158,75),(35,207,159,76),(36,208,160,77),(37,209,161,78),(38,210,162,79),(39,197,163,80),(40,198,164,81),(41,199,165,82),(42,200,166,83),(85,212,143,133),(86,213,144,134),(87,214,145,135),(88,215,146,136),(89,216,147,137),(90,217,148,138),(91,218,149,139),(92,219,150,140),(93,220,151,127),(94,221,152,128),(95,222,153,129),(96,223,154,130),(97,224,141,131),(98,211,142,132)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | ··· | 4E | 4F | 4G | 4H | 4I | 4J | ··· | 4N | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14O | 14P | 14Q | 14R | 28A | ··· | 28L | 28M | ··· | 28U |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 28 | 4 | ··· | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | D14 | 2- 1+4 | D4×D7 | D4.10D14 |
| kernel | C14.792- 1+4 | C23.11D14 | C22⋊Dic14 | Dic7.D4 | C22.D28 | C28⋊Q8 | D14⋊Q8 | C23.23D14 | C23.18D14 | C7×C22.D4 | C22×Dic14 | C2×D4⋊2D7 | C2×Dic7 | C22.D4 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C14 | C22 | C2 |
| # reps | 1 | 1 | 2 | 2 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 4 | 3 | 9 | 6 | 3 | 3 | 2 | 6 | 12 |
Matrix representation of C14.792- 1+4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 10 | 0 | 0 |
| 0 | 0 | 14 | 28 | 0 | 0 |
| 0 | 0 | 3 | 28 | 4 | 10 |
| 0 | 0 | 26 | 26 | 14 | 28 |
| 26 | 22 | 0 | 0 | 0 | 0 |
| 26 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 14 | 25 | 2 | 0 |
| 0 | 0 | 24 | 10 | 0 | 2 |
| 0 | 0 | 22 | 19 | 15 | 4 |
| 0 | 0 | 2 | 12 | 5 | 19 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 15 | 4 | 28 | 0 |
| 0 | 0 | 5 | 19 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 22 | 8 | 0 | 0 |
| 0 | 0 | 1 | 7 | 0 | 0 |
| 0 | 0 | 11 | 12 | 22 | 8 |
| 0 | 0 | 25 | 18 | 1 | 7 |
| 28 | 2 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 23 | 0 | 0 |
| 0 | 0 | 9 | 16 | 0 | 0 |
| 0 | 0 | 4 | 18 | 13 | 23 |
| 0 | 0 | 25 | 25 | 9 | 16 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,4,14,3,26,0,0,10,28,28,26,0,0,0,0,4,14,0,0,0,0,10,28],[26,26,0,0,0,0,22,3,0,0,0,0,0,0,14,24,22,2,0,0,25,10,19,12,0,0,2,0,15,5,0,0,0,2,4,19],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,15,5,0,0,0,1,4,19,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,22,1,11,25,0,0,8,7,12,18,0,0,0,0,22,1,0,0,0,0,8,7],[28,0,0,0,0,0,2,1,0,0,0,0,0,0,13,9,4,25,0,0,23,16,18,25,0,0,0,0,13,9,0,0,0,0,23,16] >;
C14.792- 1+4 in GAP, Magma, Sage, TeX
C_{14}._{79}2_-^{1+4} % in TeX
G:=Group("C14.79ES-(2,2)"); // GroupNames label
G:=SmallGroup(448,1101);
// by ID
G=gap.SmallGroup(448,1101);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,387,1123,185,136,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^4=c^2=1,d^2=e^2=b^2,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1,a*e=e*a,c*b*c=b^-1,b*d=d*b,e*b*e^-1=a^7*b,c*d=d*c,c*e=e*c,e*d*e^-1=b^2*d>;
// generators/relations