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G = SD16×C31order 496 = 24·31

Direct product of C31 and SD16

direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary

Aliases: SD16×C31, Q8⋊C62, C82C62, D4.C62, C2486C2, C62.15D4, C124.18C22, C4.2(C2×C62), (Q8×C31)⋊4C2, C2.4(D4×C31), (D4×C31).2C2, SmallGroup(496,25)

Series: Derived Chief Lower central Upper central

C1C4 — SD16×C31
C1C2C4C124Q8×C31 — SD16×C31
C1C2C4 — SD16×C31
C1C62C124 — SD16×C31

Generators and relations for SD16×C31
 G = < a,b,c | a31=b8=c2=1, ab=ba, ac=ca, cbc=b3 >

4C2
2C4
2C22
4C62
2C124
2C2×C62

Smallest permutation representation of SD16×C31
On 248 points
Generators in S248
(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)
(1 153 244 204 110 157 37 89)(2 154 245 205 111 158 38 90)(3 155 246 206 112 159 39 91)(4 125 247 207 113 160 40 92)(5 126 248 208 114 161 41 93)(6 127 218 209 115 162 42 63)(7 128 219 210 116 163 43 64)(8 129 220 211 117 164 44 65)(9 130 221 212 118 165 45 66)(10 131 222 213 119 166 46 67)(11 132 223 214 120 167 47 68)(12 133 224 215 121 168 48 69)(13 134 225 216 122 169 49 70)(14 135 226 217 123 170 50 71)(15 136 227 187 124 171 51 72)(16 137 228 188 94 172 52 73)(17 138 229 189 95 173 53 74)(18 139 230 190 96 174 54 75)(19 140 231 191 97 175 55 76)(20 141 232 192 98 176 56 77)(21 142 233 193 99 177 57 78)(22 143 234 194 100 178 58 79)(23 144 235 195 101 179 59 80)(24 145 236 196 102 180 60 81)(25 146 237 197 103 181 61 82)(26 147 238 198 104 182 62 83)(27 148 239 199 105 183 32 84)(28 149 240 200 106 184 33 85)(29 150 241 201 107 185 34 86)(30 151 242 202 108 186 35 87)(31 152 243 203 109 156 36 88)
(32 239)(33 240)(34 241)(35 242)(36 243)(37 244)(38 245)(39 246)(40 247)(41 248)(42 218)(43 219)(44 220)(45 221)(46 222)(47 223)(48 224)(49 225)(50 226)(51 227)(52 228)(53 229)(54 230)(55 231)(56 232)(57 233)(58 234)(59 235)(60 236)(61 237)(62 238)(63 162)(64 163)(65 164)(66 165)(67 166)(68 167)(69 168)(70 169)(71 170)(72 171)(73 172)(74 173)(75 174)(76 175)(77 176)(78 177)(79 178)(80 179)(81 180)(82 181)(83 182)(84 183)(85 184)(86 185)(87 186)(88 156)(89 157)(90 158)(91 159)(92 160)(93 161)(125 207)(126 208)(127 209)(128 210)(129 211)(130 212)(131 213)(132 214)(133 215)(134 216)(135 217)(136 187)(137 188)(138 189)(139 190)(140 191)(141 192)(142 193)(143 194)(144 195)(145 196)(146 197)(147 198)(148 199)(149 200)(150 201)(151 202)(152 203)(153 204)(154 205)(155 206)

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

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

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

217 conjugacy classes

class 1 2A2B4A4B8A8B31A···31AD62A···62AD62AE···62BH124A···124AD124AE···124BH248A···248BH
order122448831···3162···6262···62124···124124···124248···248
size11424221···11···14···42···24···42···2

217 irreducible representations

dim111111112222
type+++++
imageC1C2C2C2C31C62C62C62D4SD16D4×C31SD16×C31
kernelSD16×C31C248D4×C31Q8×C31SD16C8D4Q8C62C31C2C1
# reps111130303030123060

Matrix representation of SD16×C31 in GL2(𝔽1489) generated by

2960
0296
,
2061283
206206
,
10
01488
G:=sub<GL(2,GF(1489))| [296,0,0,296],[206,206,1283,206],[1,0,0,1488] >;

SD16×C31 in GAP, Magma, Sage, TeX

{\rm SD}_{16}\times C_{31}
% in TeX

G:=Group("SD16xC31");
// GroupNames label

G:=SmallGroup(496,25);
// by ID

G=gap.SmallGroup(496,25);
# by ID

G:=PCGroup([5,-2,-2,-31,-2,-2,1240,1261,7443,3728,58]);
// Polycyclic

G:=Group<a,b,c|a^31=b^8=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^3>;
// generators/relations

Export

Subgroup lattice of SD16×C31 in TeX

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