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G = C15⋊Q16order 240 = 24·3·5

1st semidirect product of C15 and Q16 acting via Q16/C4=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C151Q16, C20.7D6, C30.10D4, C12.7D10, Dic6.2D5, C60.25C22, Dic10.2S3, C4.18(S3×D5), C32(C5⋊Q16), C52(C3⋊Q16), C153C8.2C2, C6.10(C5⋊D4), C2.7(C15⋊D4), (C5×Dic6).2C2, C10.10(C3⋊D4), (C3×Dic10).2C2, SmallGroup(240,22)

Series: Derived Chief Lower central Upper central

C1C60 — C15⋊Q16
C1C5C15C30C60C3×Dic10 — C15⋊Q16
C15C30C60 — C15⋊Q16
C1C2C4

Generators and relations for C15⋊Q16
 G = < a,b,c | a15=b8=1, c2=b4, bab-1=a-1, cac-1=a11, cbc-1=b-1 >

6C4
10C4
3Q8
5Q8
15C8
2Dic3
10C12
2Dic5
6C20
15Q16
5C3×Q8
5C3⋊C8
3C52C8
3C5×Q8
2C5×Dic3
2C3×Dic5
5C3⋊Q16
3C5⋊Q16

Character table of C15⋊Q16

 class 1234A4B4C5A5B68A8B10A10B12A12B12C15A15B20A20B20C20D20E20F30A30B60A60B60C60D
 size 1122122022230302242020444412121212444444
ρ1111111111111111111111111111111    trivial
ρ21111-1-111111111-1-11111-1-1-1-1111111    linear of order 2
ρ31111-11111-1-1111111111-1-1-1-1111111    linear of order 2
ρ411111-1111-1-1111-1-111111111111111    linear of order 2
ρ5222-2002220022-20022-2-2000022-2-2-2-2    orthogonal lifted from D4
ρ622-120222-10022-1-1-1-1-1220000-1-1-1-1-1-1    orthogonal lifted from S3
ρ722-120-222-10022-111-1-1220000-1-1-1-1-1-1    orthogonal lifted from D6
ρ82222-20-1-5/2-1+5/2200-1+5/2-1-5/2200-1-5/2-1+5/2-1-5/2-1+5/21+5/21+5/21-5/21-5/2-1-5/2-1+5/2-1-5/2-1+5/2-1+5/2-1-5/2    orthogonal lifted from D10
ρ92222-20-1+5/2-1-5/2200-1-5/2-1+5/2200-1+5/2-1-5/2-1+5/2-1-5/21-5/21-5/21+5/21+5/2-1+5/2-1-5/2-1+5/2-1-5/2-1-5/2-1+5/2    orthogonal lifted from D10
ρ10222220-1+5/2-1-5/2200-1-5/2-1+5/2200-1+5/2-1-5/2-1+5/2-1-5/2-1+5/2-1+5/2-1-5/2-1-5/2-1+5/2-1-5/2-1+5/2-1-5/2-1-5/2-1+5/2    orthogonal lifted from D5
ρ11222220-1-5/2-1+5/2200-1+5/2-1-5/2200-1-5/2-1+5/2-1-5/2-1+5/2-1-5/2-1-5/2-1+5/2-1+5/2-1-5/2-1+5/2-1-5/2-1+5/2-1+5/2-1-5/2    orthogonal lifted from D5
ρ122-2200022-2-22-2-200022000000-2-20000    symplectic lifted from Q16, Schur index 2
ρ132-2200022-22-2-2-200022000000-2-20000    symplectic lifted from Q16, Schur index 2
ρ1422-1-20022-100221--3-3-1-1-2-20000-1-11111    complex lifted from C3⋊D4
ρ15222-200-1+5/2-1-5/2200-1-5/2-1+5/2-200-1+5/2-1-5/21-5/21+5/2ζ545545ζ53525352-1+5/2-1-5/21-5/21+5/21+5/21-5/2    complex lifted from C5⋊D4
ρ1622-1-20022-100221-3--3-1-1-2-20000-1-11111    complex lifted from C3⋊D4
ρ17222-200-1+5/2-1-5/2200-1-5/2-1+5/2-200-1+5/2-1-5/21-5/21+5/2545ζ5455352ζ5352-1+5/2-1-5/21-5/21+5/21+5/21-5/2    complex lifted from C5⋊D4
ρ18222-200-1-5/2-1+5/2200-1+5/2-1-5/2-200-1-5/2-1+5/21+5/21-5/2ζ53525352545ζ545-1-5/2-1+5/21+5/21-5/21-5/21+5/2    complex lifted from C5⋊D4
ρ19222-200-1-5/2-1+5/2200-1+5/2-1-5/2-200-1-5/2-1+5/21+5/21-5/25352ζ5352ζ545545-1-5/2-1+5/21+5/21-5/21-5/21+5/2    complex lifted from C5⋊D4
ρ2044-2400-1+5-1-5-200-1-5-1+5-2001-5/21+5/2-1+5-1-500001-5/21+5/21-5/21+5/21+5/21-5/2    orthogonal lifted from S3×D5
ρ2144-2400-1-5-1+5-200-1+5-1-5-2001+5/21-5/2-1-5-1+500001+5/21-5/21+5/21-5/21-5/21+5/2    orthogonal lifted from S3×D5
ρ224-4-200044200-4-4000-2-2000000220000    symplectic lifted from C3⋊Q16, Schur index 2
ρ2344-2-400-1-5-1+5-200-1+5-1-52001+5/21-5/21+51-500001+5/21-5/2-1-5/2-1+5/2-1+5/2-1-5/2    symplectic lifted from C15⋊D4, Schur index 2
ρ244-44000-1+5-1-5-4001+51-5000-1+5-1-50000001-51+50000    symplectic lifted from C5⋊Q16, Schur index 2
ρ2544-2-400-1+5-1-5-200-1-5-1+52001-5/21+5/21-51+500001-5/21+5/2-1+5/2-1-5/2-1-5/2-1+5/2    symplectic lifted from C15⋊D4, Schur index 2
ρ264-44000-1-5-1+5-4001-51+5000-1-5-1+50000001+51-50000    symplectic lifted from C5⋊Q16, Schur index 2
ρ274-4-2000-1+5-1-52001+51-50001-5/21+5/2000000-1+5/2-1-5/2-2ζ43ζ3ζ54+2ζ43ζ3ζ543ζ5443ζ543ζ3ζ53-2ζ43ζ3ζ5243ζ5343ζ524ζ3ζ53-2ζ4ζ3ζ524ζ534ζ52-2ζ4ζ3ζ54+2ζ4ζ3ζ54ζ544ζ5    complex faithful
ρ284-4-2000-1-5-1+52001-51+50001+5/21-5/2000000-1-5/2-1+5/243ζ3ζ53-2ζ43ζ3ζ5243ζ5343ζ52-2ζ4ζ3ζ54+2ζ4ζ3ζ54ζ544ζ5-2ζ43ζ3ζ54+2ζ43ζ3ζ543ζ5443ζ54ζ3ζ53-2ζ4ζ3ζ524ζ534ζ52    complex faithful
ρ294-4-2000-1+5-1-52001+51-50001-5/21+5/2000000-1+5/2-1-5/2-2ζ4ζ3ζ54+2ζ4ζ3ζ54ζ544ζ54ζ3ζ53-2ζ4ζ3ζ524ζ534ζ5243ζ3ζ53-2ζ43ζ3ζ5243ζ5343ζ52-2ζ43ζ3ζ54+2ζ43ζ3ζ543ζ5443ζ5    complex faithful
ρ304-4-2000-1-5-1+52001-51+50001+5/21-5/2000000-1-5/2-1+5/24ζ3ζ53-2ζ4ζ3ζ524ζ534ζ52-2ζ43ζ3ζ54+2ζ43ζ3ζ543ζ5443ζ5-2ζ4ζ3ζ54+2ζ4ζ3ζ54ζ544ζ543ζ3ζ53-2ζ43ζ3ζ5243ζ5343ζ52    complex faithful

Smallest permutation representation of C15⋊Q16
Regular action on 240 points
Generators in S240
(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)
(1 225 39 203 16 235 58 184)(2 224 40 202 17 234 59 183)(3 223 41 201 18 233 60 182)(4 222 42 200 19 232 46 181)(5 221 43 199 20 231 47 195)(6 220 44 198 21 230 48 194)(7 219 45 197 22 229 49 193)(8 218 31 196 23 228 50 192)(9 217 32 210 24 227 51 191)(10 216 33 209 25 226 52 190)(11 215 34 208 26 240 53 189)(12 214 35 207 27 239 54 188)(13 213 36 206 28 238 55 187)(14 212 37 205 29 237 56 186)(15 211 38 204 30 236 57 185)(61 160 120 130 77 179 102 149)(62 159 106 129 78 178 103 148)(63 158 107 128 79 177 104 147)(64 157 108 127 80 176 105 146)(65 156 109 126 81 175 91 145)(66 155 110 125 82 174 92 144)(67 154 111 124 83 173 93 143)(68 153 112 123 84 172 94 142)(69 152 113 122 85 171 95 141)(70 151 114 121 86 170 96 140)(71 165 115 135 87 169 97 139)(72 164 116 134 88 168 98 138)(73 163 117 133 89 167 99 137)(74 162 118 132 90 166 100 136)(75 161 119 131 76 180 101 150)
(1 90 16 74)(2 86 17 70)(3 82 18 66)(4 78 19 62)(5 89 20 73)(6 85 21 69)(7 81 22 65)(8 77 23 61)(9 88 24 72)(10 84 25 68)(11 80 26 64)(12 76 27 75)(13 87 28 71)(14 83 29 67)(15 79 30 63)(31 120 50 102)(32 116 51 98)(33 112 52 94)(34 108 53 105)(35 119 54 101)(36 115 55 97)(37 111 56 93)(38 107 57 104)(39 118 58 100)(40 114 59 96)(41 110 60 92)(42 106 46 103)(43 117 47 99)(44 113 48 95)(45 109 49 91)(121 234 140 224)(122 230 141 220)(123 226 142 216)(124 237 143 212)(125 233 144 223)(126 229 145 219)(127 240 146 215)(128 236 147 211)(129 232 148 222)(130 228 149 218)(131 239 150 214)(132 235 136 225)(133 231 137 221)(134 227 138 217)(135 238 139 213)(151 183 170 202)(152 194 171 198)(153 190 172 209)(154 186 173 205)(155 182 174 201)(156 193 175 197)(157 189 176 208)(158 185 177 204)(159 181 178 200)(160 192 179 196)(161 188 180 207)(162 184 166 203)(163 195 167 199)(164 191 168 210)(165 187 169 206)

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

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

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

C15⋊Q16 is a maximal subgroup of
Dic10.D6  Dic6.D10  D30.3D4  D30.4D4  D20.34D6  D20.37D6  D12.37D10  C60.8C23  C60.10C23  C60.16C23  C60.19C23  D5×C3⋊Q16  S3×C5⋊Q16  C60.39C23  C60.44C23
C15⋊Q16 is a maximal quotient of
C30.Q16  Dic6⋊Dic5  C30.20D8

Matrix representation of C15⋊Q16 in GL6(𝔽241)

100000
010000
001905100
0019024000
0000239192
0000641
,
02190000
112190000
001318000
0014711000
000013198
0000179110
,
25830000
1872160000
00240000
00024000
0000160117
00008481

G:=sub<GL(6,GF(241))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,190,190,0,0,0,0,51,240,0,0,0,0,0,0,239,64,0,0,0,0,192,1],[0,11,0,0,0,0,219,219,0,0,0,0,0,0,131,147,0,0,0,0,80,110,0,0,0,0,0,0,131,179,0,0,0,0,98,110],[25,187,0,0,0,0,83,216,0,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,0,160,84,0,0,0,0,117,81] >;

C15⋊Q16 in GAP, Magma, Sage, TeX

C_{15}\rtimes Q_{16}
% in TeX

G:=Group("C15:Q16");
// GroupNames label

G:=SmallGroup(240,22);
// by ID

G=gap.SmallGroup(240,22);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-3,-5,48,73,55,218,116,50,490,6917]);
// Polycyclic

G:=Group<a,b,c|a^15=b^8=1,c^2=b^4,b*a*b^-1=a^-1,c*a*c^-1=a^11,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C15⋊Q16 in TeX
Character table of C15⋊Q16 in TeX

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