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G = C3×C93order 279 = 32·31

Abelian group of type [3,93]

direct product, abelian, monomial, 3-elementary

Aliases: C3×C93, SmallGroup(279,4)

Series: Derived Chief Lower central Upper central

C1 — C3×C93
C1C31C93 — C3×C93
C1 — C3×C93
C1 — C3×C93

Generators and relations for C3×C93
 G = < a,b | a3=b93=1, ab=ba >


Smallest permutation representation of C3×C93
Regular action on 279 points
Generators in S279
(1 273 178)(2 274 179)(3 275 180)(4 276 181)(5 277 182)(6 278 183)(7 279 184)(8 187 185)(9 188 186)(10 189 94)(11 190 95)(12 191 96)(13 192 97)(14 193 98)(15 194 99)(16 195 100)(17 196 101)(18 197 102)(19 198 103)(20 199 104)(21 200 105)(22 201 106)(23 202 107)(24 203 108)(25 204 109)(26 205 110)(27 206 111)(28 207 112)(29 208 113)(30 209 114)(31 210 115)(32 211 116)(33 212 117)(34 213 118)(35 214 119)(36 215 120)(37 216 121)(38 217 122)(39 218 123)(40 219 124)(41 220 125)(42 221 126)(43 222 127)(44 223 128)(45 224 129)(46 225 130)(47 226 131)(48 227 132)(49 228 133)(50 229 134)(51 230 135)(52 231 136)(53 232 137)(54 233 138)(55 234 139)(56 235 140)(57 236 141)(58 237 142)(59 238 143)(60 239 144)(61 240 145)(62 241 146)(63 242 147)(64 243 148)(65 244 149)(66 245 150)(67 246 151)(68 247 152)(69 248 153)(70 249 154)(71 250 155)(72 251 156)(73 252 157)(74 253 158)(75 254 159)(76 255 160)(77 256 161)(78 257 162)(79 258 163)(80 259 164)(81 260 165)(82 261 166)(83 262 167)(84 263 168)(85 264 169)(86 265 170)(87 266 171)(88 267 172)(89 268 173)(90 269 174)(91 270 175)(92 271 176)(93 272 177)
(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)(187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279)

G:=sub<Sym(279)| (1,273,178)(2,274,179)(3,275,180)(4,276,181)(5,277,182)(6,278,183)(7,279,184)(8,187,185)(9,188,186)(10,189,94)(11,190,95)(12,191,96)(13,192,97)(14,193,98)(15,194,99)(16,195,100)(17,196,101)(18,197,102)(19,198,103)(20,199,104)(21,200,105)(22,201,106)(23,202,107)(24,203,108)(25,204,109)(26,205,110)(27,206,111)(28,207,112)(29,208,113)(30,209,114)(31,210,115)(32,211,116)(33,212,117)(34,213,118)(35,214,119)(36,215,120)(37,216,121)(38,217,122)(39,218,123)(40,219,124)(41,220,125)(42,221,126)(43,222,127)(44,223,128)(45,224,129)(46,225,130)(47,226,131)(48,227,132)(49,228,133)(50,229,134)(51,230,135)(52,231,136)(53,232,137)(54,233,138)(55,234,139)(56,235,140)(57,236,141)(58,237,142)(59,238,143)(60,239,144)(61,240,145)(62,241,146)(63,242,147)(64,243,148)(65,244,149)(66,245,150)(67,246,151)(68,247,152)(69,248,153)(70,249,154)(71,250,155)(72,251,156)(73,252,157)(74,253,158)(75,254,159)(76,255,160)(77,256,161)(78,257,162)(79,258,163)(80,259,164)(81,260,165)(82,261,166)(83,262,167)(84,263,168)(85,264,169)(86,265,170)(87,266,171)(88,267,172)(89,268,173)(90,269,174)(91,270,175)(92,271,176)(93,272,177), (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)(187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279)>;

G:=Group( (1,273,178)(2,274,179)(3,275,180)(4,276,181)(5,277,182)(6,278,183)(7,279,184)(8,187,185)(9,188,186)(10,189,94)(11,190,95)(12,191,96)(13,192,97)(14,193,98)(15,194,99)(16,195,100)(17,196,101)(18,197,102)(19,198,103)(20,199,104)(21,200,105)(22,201,106)(23,202,107)(24,203,108)(25,204,109)(26,205,110)(27,206,111)(28,207,112)(29,208,113)(30,209,114)(31,210,115)(32,211,116)(33,212,117)(34,213,118)(35,214,119)(36,215,120)(37,216,121)(38,217,122)(39,218,123)(40,219,124)(41,220,125)(42,221,126)(43,222,127)(44,223,128)(45,224,129)(46,225,130)(47,226,131)(48,227,132)(49,228,133)(50,229,134)(51,230,135)(52,231,136)(53,232,137)(54,233,138)(55,234,139)(56,235,140)(57,236,141)(58,237,142)(59,238,143)(60,239,144)(61,240,145)(62,241,146)(63,242,147)(64,243,148)(65,244,149)(66,245,150)(67,246,151)(68,247,152)(69,248,153)(70,249,154)(71,250,155)(72,251,156)(73,252,157)(74,253,158)(75,254,159)(76,255,160)(77,256,161)(78,257,162)(79,258,163)(80,259,164)(81,260,165)(82,261,166)(83,262,167)(84,263,168)(85,264,169)(86,265,170)(87,266,171)(88,267,172)(89,268,173)(90,269,174)(91,270,175)(92,271,176)(93,272,177), (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)(187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279) );

G=PermutationGroup([(1,273,178),(2,274,179),(3,275,180),(4,276,181),(5,277,182),(6,278,183),(7,279,184),(8,187,185),(9,188,186),(10,189,94),(11,190,95),(12,191,96),(13,192,97),(14,193,98),(15,194,99),(16,195,100),(17,196,101),(18,197,102),(19,198,103),(20,199,104),(21,200,105),(22,201,106),(23,202,107),(24,203,108),(25,204,109),(26,205,110),(27,206,111),(28,207,112),(29,208,113),(30,209,114),(31,210,115),(32,211,116),(33,212,117),(34,213,118),(35,214,119),(36,215,120),(37,216,121),(38,217,122),(39,218,123),(40,219,124),(41,220,125),(42,221,126),(43,222,127),(44,223,128),(45,224,129),(46,225,130),(47,226,131),(48,227,132),(49,228,133),(50,229,134),(51,230,135),(52,231,136),(53,232,137),(54,233,138),(55,234,139),(56,235,140),(57,236,141),(58,237,142),(59,238,143),(60,239,144),(61,240,145),(62,241,146),(63,242,147),(64,243,148),(65,244,149),(66,245,150),(67,246,151),(68,247,152),(69,248,153),(70,249,154),(71,250,155),(72,251,156),(73,252,157),(74,253,158),(75,254,159),(76,255,160),(77,256,161),(78,257,162),(79,258,163),(80,259,164),(81,260,165),(82,261,166),(83,262,167),(84,263,168),(85,264,169),(86,265,170),(87,266,171),(88,267,172),(89,268,173),(90,269,174),(91,270,175),(92,271,176),(93,272,177)], [(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),(187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279)])

279 conjugacy classes

class 1 3A···3H31A···31AD93A···93IF
order13···331···3193···93
size11···11···11···1

279 irreducible representations

dim1111
type+
imageC1C3C31C93
kernelC3×C93C93C32C3
# reps1830240

Matrix representation of C3×C93 in GL2(𝔽373) generated by

2840
01
,
2830
016
G:=sub<GL(2,GF(373))| [284,0,0,1],[283,0,0,16] >;

C3×C93 in GAP, Magma, Sage, TeX

C_3\times C_{93}
% in TeX

G:=Group("C3xC93");
// GroupNames label

G:=SmallGroup(279,4);
// by ID

G=gap.SmallGroup(279,4);
# by ID

G:=PCGroup([3,-3,-3,-31]);
// Polycyclic

G:=Group<a,b|a^3=b^93=1,a*b=b*a>;
// generators/relations

Export

Subgroup lattice of C3×C93 in TeX

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