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G = C3×C20.10D4order 480 = 25·3·5

Direct product of C3 and C20.10D4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C3×C20.10D4, C60.120D4, (C6×Q8).7D5, (C2×C60).23C4, C20.10(C3×D4), (Q8×C10).6C6, (Q8×C30).7C2, (C2×C20).12C12, (C2×C12).1Dic5, C4.Dic5.4C6, (C2×C12).214D10, C12.94(C5⋊D4), C22.4(C6×Dic5), C1511(C4.10D4), (C2×C60).282C22, C6.26(C23.D5), C30.114(C22⋊C4), (C2×C4).4(C6×D5), (C2×C4).(C3×Dic5), C53(C3×C4.10D4), C4.15(C3×C5⋊D4), (C2×Q8).4(C3×D5), (C2×C20).18(C2×C6), (C2×C10).51(C2×C12), (C2×C30).187(C2×C4), C2.7(C3×C23.D5), C10.28(C3×C22⋊C4), (C2×C6).22(C2×Dic5), (C3×C4.Dic5).8C2, SmallGroup(480,114)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C3×C20.10D4
C1C5C10C2×C10C2×C20C2×C60C3×C4.Dic5 — C3×C20.10D4
C5C10C2×C10 — C3×C20.10D4
C1C6C2×C12C6×Q8

Generators and relations for C3×C20.10D4
 G = < a,b,c,d | a3=b20=1, c4=b10, d2=b5, ab=ba, ac=ca, ad=da, cbc-1=b-1, dbd-1=b9, dcd-1=b5c3 >

Subgroups: 160 in 76 conjugacy classes, 42 normal (22 characteristic)
C1, C2, C2, C3, C4 [×2], C4 [×2], C22, C5, C6, C6, C8 [×2], C2×C4, C2×C4 [×2], Q8 [×2], C10, C10, C12 [×2], C12 [×2], C2×C6, C15, M4(2) [×2], C2×Q8, C20 [×2], C20 [×2], C2×C10, C24 [×2], C2×C12, C2×C12 [×2], C3×Q8 [×2], C30, C30, C4.10D4, C52C8 [×2], C2×C20, C2×C20 [×2], C5×Q8 [×2], C3×M4(2) [×2], C6×Q8, C60 [×2], C60 [×2], C2×C30, C4.Dic5 [×2], Q8×C10, C3×C4.10D4, C3×C52C8 [×2], C2×C60, C2×C60 [×2], Q8×C15 [×2], C20.10D4, C3×C4.Dic5 [×2], Q8×C30, C3×C20.10D4
Quotients: C1, C2 [×3], C3, C4 [×2], C22, C6 [×3], C2×C4, D4 [×2], D5, C12 [×2], C2×C6, C22⋊C4, Dic5 [×2], D10, C2×C12, C3×D4 [×2], C3×D5, C4.10D4, C2×Dic5, C5⋊D4 [×2], C3×C22⋊C4, C3×Dic5 [×2], C6×D5, C23.D5, C3×C4.10D4, C6×Dic5, C3×C5⋊D4 [×2], C20.10D4, C3×C23.D5, C3×C20.10D4

Smallest permutation representation of C3×C20.10D4
On 240 points
Generators in S240
(1 44 24)(2 45 25)(3 46 26)(4 47 27)(5 48 28)(6 49 29)(7 50 30)(8 51 31)(9 52 32)(10 53 33)(11 54 34)(12 55 35)(13 56 36)(14 57 37)(15 58 38)(16 59 39)(17 60 40)(18 41 21)(19 42 22)(20 43 23)(61 112 92)(62 113 93)(63 114 94)(64 115 95)(65 116 96)(66 117 97)(67 118 98)(68 119 99)(69 120 100)(70 101 81)(71 102 82)(72 103 83)(73 104 84)(74 105 85)(75 106 86)(76 107 87)(77 108 88)(78 109 89)(79 110 90)(80 111 91)(121 166 141)(122 167 142)(123 168 143)(124 169 144)(125 170 145)(126 171 146)(127 172 147)(128 173 148)(129 174 149)(130 175 150)(131 176 151)(132 177 152)(133 178 153)(134 179 154)(135 180 155)(136 161 156)(137 162 157)(138 163 158)(139 164 159)(140 165 160)(181 221 216)(182 222 217)(183 223 218)(184 224 219)(185 225 220)(186 226 201)(187 227 202)(188 228 203)(189 229 204)(190 230 205)(191 231 206)(192 232 207)(193 233 208)(194 234 209)(195 235 210)(196 236 211)(197 237 212)(198 238 213)(199 239 214)(200 240 215)
(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)
(1 186 16 191 11 196 6 181)(2 185 17 190 12 195 7 200)(3 184 18 189 13 194 8 199)(4 183 19 188 14 193 9 198)(5 182 20 187 15 192 10 197)(21 204 36 209 31 214 26 219)(22 203 37 208 32 213 27 218)(23 202 38 207 33 212 28 217)(24 201 39 206 34 211 29 216)(25 220 40 205 35 210 30 215)(41 229 56 234 51 239 46 224)(42 228 57 233 52 238 47 223)(43 227 58 232 53 237 48 222)(44 226 59 231 54 236 49 221)(45 225 60 230 55 235 50 240)(61 128 76 133 71 138 66 123)(62 127 77 132 72 137 67 122)(63 126 78 131 73 136 68 121)(64 125 79 130 74 135 69 140)(65 124 80 129 75 134 70 139)(81 159 96 144 91 149 86 154)(82 158 97 143 92 148 87 153)(83 157 98 142 93 147 88 152)(84 156 99 141 94 146 89 151)(85 155 100 160 95 145 90 150)(101 164 116 169 111 174 106 179)(102 163 117 168 112 173 107 178)(103 162 118 167 113 172 108 177)(104 161 119 166 114 171 109 176)(105 180 120 165 115 170 110 175)
(1 121 6 126 11 131 16 136)(2 130 7 135 12 140 17 125)(3 139 8 124 13 129 18 134)(4 128 9 133 14 138 19 123)(5 137 10 122 15 127 20 132)(21 154 26 159 31 144 36 149)(22 143 27 148 32 153 37 158)(23 152 28 157 33 142 38 147)(24 141 29 146 34 151 39 156)(25 150 30 155 35 160 40 145)(41 179 46 164 51 169 56 174)(42 168 47 173 52 178 57 163)(43 177 48 162 53 167 58 172)(44 166 49 171 54 176 59 161)(45 175 50 180 55 165 60 170)(61 193 66 198 71 183 76 188)(62 182 67 187 72 192 77 197)(63 191 68 196 73 181 78 186)(64 200 69 185 74 190 79 195)(65 189 70 194 75 199 80 184)(81 209 86 214 91 219 96 204)(82 218 87 203 92 208 97 213)(83 207 88 212 93 217 98 202)(84 216 89 201 94 206 99 211)(85 205 90 210 95 215 100 220)(101 234 106 239 111 224 116 229)(102 223 107 228 112 233 117 238)(103 232 108 237 113 222 118 227)(104 221 109 226 114 231 119 236)(105 230 110 235 115 240 120 225)

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

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

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

93 conjugacy classes

class 1 2A2B3A3B4A4B4C4D5A5B6A6B6C6D8A8B8C8D10A···10F12A12B12C12D12E12F12G12H15A15B15C15D20A···20L24A···24H30A···30L60A···60X
order122334444556666888810···1012121212121212121515151520···2024···2430···3060···60
size112112244221122202020202···22222444422224···420···202···24···4

93 irreducible representations

dim1111111122222222224444
type+++++-+-
imageC1C2C2C3C4C6C6C12D4D5Dic5D10C3×D4C3×D5C5⋊D4C3×Dic5C6×D5C3×C5⋊D4C4.10D4C3×C4.10D4C20.10D4C3×C20.10D4
kernelC3×C20.10D4C3×C4.Dic5Q8×C30C20.10D4C2×C60C4.Dic5Q8×C10C2×C20C60C6×Q8C2×C12C2×C12C20C2×Q8C12C2×C4C2×C4C4C15C5C3C1
# reps12124428224244884161248

Matrix representation of C3×C20.10D4 in GL6(𝔽241)

1500000
0150000
001000
000100
000010
000001
,
981170000
0910000
000100
00240000
00153001
000882400
,
212190000
422200000
005325183214
0022315421458
0017010618818
0010620521687
,
2202400000
199210000
00152882390
00881520239
000089153
001015389

G:=sub<GL(6,GF(241))| [15,0,0,0,0,0,0,15,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[98,0,0,0,0,0,117,91,0,0,0,0,0,0,0,240,153,0,0,0,1,0,0,88,0,0,0,0,0,240,0,0,0,0,1,0],[21,42,0,0,0,0,219,220,0,0,0,0,0,0,53,223,170,106,0,0,25,154,106,205,0,0,183,214,188,216,0,0,214,58,18,87],[220,199,0,0,0,0,240,21,0,0,0,0,0,0,152,88,0,1,0,0,88,152,0,0,0,0,239,0,89,153,0,0,0,239,153,89] >;

C3×C20.10D4 in GAP, Magma, Sage, TeX

C_3\times C_{20}._{10}D_4
% in TeX

G:=Group("C3xC20.10D4");
// GroupNames label

G:=SmallGroup(480,114);
// by ID

G=gap.SmallGroup(480,114);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,84,365,344,850,136,2524,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^3=b^20=1,c^4=b^10,d^2=b^5,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,d*b*d^-1=b^9,d*c*d^-1=b^5*c^3>;
// generators/relations

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