G = C10.362+ 1+4 order 320 = 26·5
36th non-split extension by C10 of 2+ 1+4 acting via 2+ 1+4/C2×D4=C2
metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C10.362+ 1+4, C10.712- 1+4, C20⋊Q8⋊19C2, C4⋊D4.9D5, C4⋊C4.179D10, (D4×Dic5)⋊19C2, (C2×D4).91D10, C22⋊C4.7D10, (C2×C20).37C23, Dic5⋊3Q8⋊22C2, C20.202(C4○D4), C20.17D4⋊16C2, C4.68(D4⋊2D5), C20.48D4⋊32C2, (C2×C10).147C24, (C22×C4).222D10, C2.38(D4⋊6D10), C23.13(C22×D5), (D4×C10).121C22, C23.D10⋊17C2, C23.18D10⋊8C2, C4⋊Dic5.310C22, (C2×Dic5).68C23, C22.168(C23×D5), Dic5.14D4⋊18C2, C23.D5.24C22, C23.21D10⋊25C2, (C22×C20).239C22, (C22×C10).185C23, C5⋊4(C22.36C24), (C4×Dic5).102C22, C10.D4.17C22, C2.29(D4.10D10), (C2×Dic10).159C22, (C22×Dic5).108C22, C10.83(C2×C4○D4), (C5×C4⋊D4).9C2, C2.35(C2×D4⋊2D5), (C2×C4).36(C22×D5), (C5×C4⋊C4).143C22, (C5×C22⋊C4).12C22, SmallGroup(320,1275)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C10.362+ 1+4
G = < a,b,c,d,e | a10=b4=c2=1, d2=e2=a5b2, bab-1=dad-1=a-1, ac=ca, ae=ea, cbc=a5b-1, dbd-1=a5b, be=eb, dcd-1=a5c, ce=ec, ede-1=a5b2d >
Subgroups: 670 in 216 conjugacy classes, 95 normal (43 characteristic)
C1, C2, C2, C4, C4, C22, C22, C5, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C10, C10, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, Dic5, C20, C20, C2×C10, C2×C10, C42⋊C2, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, C4⋊Q8, Dic10, C2×Dic5, C2×Dic5, C2×Dic5, C2×C20, C2×C20, C2×C20, C5×D4, C22×C10, C22×C10, C22.36C24, C4×Dic5, C4×Dic5, C10.D4, C4⋊Dic5, C23.D5, C23.D5, C5×C22⋊C4, C5×C4⋊C4, C2×Dic10, C2×Dic10, C22×Dic5, C22×C20, D4×C10, D4×C10, Dic5.14D4, C23.D10, Dic5⋊3Q8, C20⋊Q8, C20.48D4, C23.21D10, D4×Dic5, C23.18D10, C20.17D4, C20.17D4, C5×C4⋊D4, C10.362+ 1+4
Quotients: C1, C2, C22, C23, D5, C4○D4, C24, D10, C2×C4○D4, 2+ 1+4, 2- 1+4, C22×D5, C22.36C24, D4⋊2D5, C23×D5, C2×D4⋊2D5, D4⋊6D10, D4.10D10, C10.362+ 1+4
►On 160 points
Generators in S160
(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)
(1 157 25 20)(2 156 26 19)(3 155 27 18)(4 154 28 17)(5 153 29 16)(6 152 30 15)(7 151 21 14)(8 160 22 13)(9 159 23 12)(10 158 24 11)(31 134 48 142)(32 133 49 141)(33 132 50 150)(34 131 41 149)(35 140 42 148)(36 139 43 147)(37 138 44 146)(38 137 45 145)(39 136 46 144)(40 135 47 143)(51 127 68 119)(52 126 69 118)(53 125 70 117)(54 124 61 116)(55 123 62 115)(56 122 63 114)(57 121 64 113)(58 130 65 112)(59 129 66 111)(60 128 67 120)(71 99 89 107)(72 98 90 106)(73 97 81 105)(74 96 82 104)(75 95 83 103)(76 94 84 102)(77 93 85 101)(78 92 86 110)(79 91 87 109)(80 100 88 108)
(11 153)(12 154)(13 155)(14 156)(15 157)(16 158)(17 159)(18 160)(19 151)(20 152)(31 48)(32 49)(33 50)(34 41)(35 42)(36 43)(37 44)(38 45)(39 46)(40 47)(51 68)(52 69)(53 70)(54 61)(55 62)(56 63)(57 64)(58 65)(59 66)(60 67)(91 104)(92 105)(93 106)(94 107)(95 108)(96 109)(97 110)(98 101)(99 102)(100 103)(111 116)(112 117)(113 118)(114 119)(115 120)(121 126)(122 127)(123 128)(124 129)(125 130)(131 136)(132 137)(133 138)(134 139)(135 140)(141 146)(142 147)(143 148)(144 149)(145 150)
(1 137 30 150)(2 136 21 149)(3 135 22 148)(4 134 23 147)(5 133 24 146)(6 132 25 145)(7 131 26 144)(8 140 27 143)(9 139 28 142)(10 138 29 141)(11 32 153 44)(12 31 154 43)(13 40 155 42)(14 39 156 41)(15 38 157 50)(16 37 158 49)(17 36 159 48)(18 35 160 47)(19 34 151 46)(20 33 152 45)(51 94 63 107)(52 93 64 106)(53 92 65 105)(54 91 66 104)(55 100 67 103)(56 99 68 102)(57 98 69 101)(58 97 70 110)(59 96 61 109)(60 95 62 108)(71 122 84 119)(72 121 85 118)(73 130 86 117)(74 129 87 116)(75 128 88 115)(76 127 89 114)(77 126 90 113)(78 125 81 112)(79 124 82 111)(80 123 83 120)
(1 86 30 73)(2 87 21 74)(3 88 22 75)(4 89 23 76)(5 90 24 77)(6 81 25 78)(7 82 26 79)(8 83 27 80)(9 84 28 71)(10 85 29 72)(11 93 153 106)(12 94 154 107)(13 95 155 108)(14 96 156 109)(15 97 157 110)(16 98 158 101)(17 99 159 102)(18 100 160 103)(19 91 151 104)(20 92 152 105)(31 51 43 63)(32 52 44 64)(33 53 45 65)(34 54 46 66)(35 55 47 67)(36 56 48 68)(37 57 49 69)(38 58 50 70)(39 59 41 61)(40 60 42 62)(111 131 124 144)(112 132 125 145)(113 133 126 146)(114 134 127 147)(115 135 128 148)(116 136 129 149)(117 137 130 150)(118 138 121 141)(119 139 122 142)(120 140 123 143)
G:=sub<Sym(160)| (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), (1,157,25,20)(2,156,26,19)(3,155,27,18)(4,154,28,17)(5,153,29,16)(6,152,30,15)(7,151,21,14)(8,160,22,13)(9,159,23,12)(10,158,24,11)(31,134,48,142)(32,133,49,141)(33,132,50,150)(34,131,41,149)(35,140,42,148)(36,139,43,147)(37,138,44,146)(38,137,45,145)(39,136,46,144)(40,135,47,143)(51,127,68,119)(52,126,69,118)(53,125,70,117)(54,124,61,116)(55,123,62,115)(56,122,63,114)(57,121,64,113)(58,130,65,112)(59,129,66,111)(60,128,67,120)(71,99,89,107)(72,98,90,106)(73,97,81,105)(74,96,82,104)(75,95,83,103)(76,94,84,102)(77,93,85,101)(78,92,86,110)(79,91,87,109)(80,100,88,108), (11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,159)(18,160)(19,151)(20,152)(31,48)(32,49)(33,50)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(51,68)(52,69)(53,70)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66)(60,67)(91,104)(92,105)(93,106)(94,107)(95,108)(96,109)(97,110)(98,101)(99,102)(100,103)(111,116)(112,117)(113,118)(114,119)(115,120)(121,126)(122,127)(123,128)(124,129)(125,130)(131,136)(132,137)(133,138)(134,139)(135,140)(141,146)(142,147)(143,148)(144,149)(145,150), (1,137,30,150)(2,136,21,149)(3,135,22,148)(4,134,23,147)(5,133,24,146)(6,132,25,145)(7,131,26,144)(8,140,27,143)(9,139,28,142)(10,138,29,141)(11,32,153,44)(12,31,154,43)(13,40,155,42)(14,39,156,41)(15,38,157,50)(16,37,158,49)(17,36,159,48)(18,35,160,47)(19,34,151,46)(20,33,152,45)(51,94,63,107)(52,93,64,106)(53,92,65,105)(54,91,66,104)(55,100,67,103)(56,99,68,102)(57,98,69,101)(58,97,70,110)(59,96,61,109)(60,95,62,108)(71,122,84,119)(72,121,85,118)(73,130,86,117)(74,129,87,116)(75,128,88,115)(76,127,89,114)(77,126,90,113)(78,125,81,112)(79,124,82,111)(80,123,83,120), (1,86,30,73)(2,87,21,74)(3,88,22,75)(4,89,23,76)(5,90,24,77)(6,81,25,78)(7,82,26,79)(8,83,27,80)(9,84,28,71)(10,85,29,72)(11,93,153,106)(12,94,154,107)(13,95,155,108)(14,96,156,109)(15,97,157,110)(16,98,158,101)(17,99,159,102)(18,100,160,103)(19,91,151,104)(20,92,152,105)(31,51,43,63)(32,52,44,64)(33,53,45,65)(34,54,46,66)(35,55,47,67)(36,56,48,68)(37,57,49,69)(38,58,50,70)(39,59,41,61)(40,60,42,62)(111,131,124,144)(112,132,125,145)(113,133,126,146)(114,134,127,147)(115,135,128,148)(116,136,129,149)(117,137,130,150)(118,138,121,141)(119,139,122,142)(120,140,123,143)>;
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), (1,157,25,20)(2,156,26,19)(3,155,27,18)(4,154,28,17)(5,153,29,16)(6,152,30,15)(7,151,21,14)(8,160,22,13)(9,159,23,12)(10,158,24,11)(31,134,48,142)(32,133,49,141)(33,132,50,150)(34,131,41,149)(35,140,42,148)(36,139,43,147)(37,138,44,146)(38,137,45,145)(39,136,46,144)(40,135,47,143)(51,127,68,119)(52,126,69,118)(53,125,70,117)(54,124,61,116)(55,123,62,115)(56,122,63,114)(57,121,64,113)(58,130,65,112)(59,129,66,111)(60,128,67,120)(71,99,89,107)(72,98,90,106)(73,97,81,105)(74,96,82,104)(75,95,83,103)(76,94,84,102)(77,93,85,101)(78,92,86,110)(79,91,87,109)(80,100,88,108), (11,153)(12,154)(13,155)(14,156)(15,157)(16,158)(17,159)(18,160)(19,151)(20,152)(31,48)(32,49)(33,50)(34,41)(35,42)(36,43)(37,44)(38,45)(39,46)(40,47)(51,68)(52,69)(53,70)(54,61)(55,62)(56,63)(57,64)(58,65)(59,66)(60,67)(91,104)(92,105)(93,106)(94,107)(95,108)(96,109)(97,110)(98,101)(99,102)(100,103)(111,116)(112,117)(113,118)(114,119)(115,120)(121,126)(122,127)(123,128)(124,129)(125,130)(131,136)(132,137)(133,138)(134,139)(135,140)(141,146)(142,147)(143,148)(144,149)(145,150), (1,137,30,150)(2,136,21,149)(3,135,22,148)(4,134,23,147)(5,133,24,146)(6,132,25,145)(7,131,26,144)(8,140,27,143)(9,139,28,142)(10,138,29,141)(11,32,153,44)(12,31,154,43)(13,40,155,42)(14,39,156,41)(15,38,157,50)(16,37,158,49)(17,36,159,48)(18,35,160,47)(19,34,151,46)(20,33,152,45)(51,94,63,107)(52,93,64,106)(53,92,65,105)(54,91,66,104)(55,100,67,103)(56,99,68,102)(57,98,69,101)(58,97,70,110)(59,96,61,109)(60,95,62,108)(71,122,84,119)(72,121,85,118)(73,130,86,117)(74,129,87,116)(75,128,88,115)(76,127,89,114)(77,126,90,113)(78,125,81,112)(79,124,82,111)(80,123,83,120), (1,86,30,73)(2,87,21,74)(3,88,22,75)(4,89,23,76)(5,90,24,77)(6,81,25,78)(7,82,26,79)(8,83,27,80)(9,84,28,71)(10,85,29,72)(11,93,153,106)(12,94,154,107)(13,95,155,108)(14,96,156,109)(15,97,157,110)(16,98,158,101)(17,99,159,102)(18,100,160,103)(19,91,151,104)(20,92,152,105)(31,51,43,63)(32,52,44,64)(33,53,45,65)(34,54,46,66)(35,55,47,67)(36,56,48,68)(37,57,49,69)(38,58,50,70)(39,59,41,61)(40,60,42,62)(111,131,124,144)(112,132,125,145)(113,133,126,146)(114,134,127,147)(115,135,128,148)(116,136,129,149)(117,137,130,150)(118,138,121,141)(119,139,122,142)(120,140,123,143) );
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)], [(1,157,25,20),(2,156,26,19),(3,155,27,18),(4,154,28,17),(5,153,29,16),(6,152,30,15),(7,151,21,14),(8,160,22,13),(9,159,23,12),(10,158,24,11),(31,134,48,142),(32,133,49,141),(33,132,50,150),(34,131,41,149),(35,140,42,148),(36,139,43,147),(37,138,44,146),(38,137,45,145),(39,136,46,144),(40,135,47,143),(51,127,68,119),(52,126,69,118),(53,125,70,117),(54,124,61,116),(55,123,62,115),(56,122,63,114),(57,121,64,113),(58,130,65,112),(59,129,66,111),(60,128,67,120),(71,99,89,107),(72,98,90,106),(73,97,81,105),(74,96,82,104),(75,95,83,103),(76,94,84,102),(77,93,85,101),(78,92,86,110),(79,91,87,109),(80,100,88,108)], [(11,153),(12,154),(13,155),(14,156),(15,157),(16,158),(17,159),(18,160),(19,151),(20,152),(31,48),(32,49),(33,50),(34,41),(35,42),(36,43),(37,44),(38,45),(39,46),(40,47),(51,68),(52,69),(53,70),(54,61),(55,62),(56,63),(57,64),(58,65),(59,66),(60,67),(91,104),(92,105),(93,106),(94,107),(95,108),(96,109),(97,110),(98,101),(99,102),(100,103),(111,116),(112,117),(113,118),(114,119),(115,120),(121,126),(122,127),(123,128),(124,129),(125,130),(131,136),(132,137),(133,138),(134,139),(135,140),(141,146),(142,147),(143,148),(144,149),(145,150)], [(1,137,30,150),(2,136,21,149),(3,135,22,148),(4,134,23,147),(5,133,24,146),(6,132,25,145),(7,131,26,144),(8,140,27,143),(9,139,28,142),(10,138,29,141),(11,32,153,44),(12,31,154,43),(13,40,155,42),(14,39,156,41),(15,38,157,50),(16,37,158,49),(17,36,159,48),(18,35,160,47),(19,34,151,46),(20,33,152,45),(51,94,63,107),(52,93,64,106),(53,92,65,105),(54,91,66,104),(55,100,67,103),(56,99,68,102),(57,98,69,101),(58,97,70,110),(59,96,61,109),(60,95,62,108),(71,122,84,119),(72,121,85,118),(73,130,86,117),(74,129,87,116),(75,128,88,115),(76,127,89,114),(77,126,90,113),(78,125,81,112),(79,124,82,111),(80,123,83,120)], [(1,86,30,73),(2,87,21,74),(3,88,22,75),(4,89,23,76),(5,90,24,77),(6,81,25,78),(7,82,26,79),(8,83,27,80),(9,84,28,71),(10,85,29,72),(11,93,153,106),(12,94,154,107),(13,95,155,108),(14,96,156,109),(15,97,157,110),(16,98,158,101),(17,99,159,102),(18,100,160,103),(19,91,151,104),(20,92,152,105),(31,51,43,63),(32,52,44,64),(33,53,45,65),(34,54,46,66),(35,55,47,67),(36,56,48,68),(37,57,49,69),(38,58,50,70),(39,59,41,61),(40,60,42,62),(111,131,124,144),(112,132,125,145),(113,133,126,146),(114,134,127,147),(115,135,128,148),(116,136,129,149),(117,137,130,150),(118,138,121,141),(119,139,122,142),(120,140,123,143)]])
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | ··· | 4O | 5A | 5B | 10A | ··· | 10F | 10G | 10H | 10I | 10J | 10K | 10L | 10M | 10N | 20A | ··· | 20H | 20I | 20J | 20K | 20L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 5 | 5 | 10 | ··· | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 20 | 20 | 20 | 20 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 2 | 2 | 4 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 2 | 2 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 4 | ··· | 4 | 8 | 8 | 8 | 8 |
50 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D5 | C4○D4 | D10 | D10 | D10 | D10 | 2+ 1+4 | 2- 1+4 | D4⋊2D5 | D4⋊6D10 | D4.10D10 |
| kernel | C10.362+ 1+4 | Dic5.14D4 | C23.D10 | Dic5⋊3Q8 | C20⋊Q8 | C20.48D4 | C23.21D10 | D4×Dic5 | C23.18D10 | C20.17D4 | C5×C4⋊D4 | C4⋊D4 | C20 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C10 | C10 | C4 | C2 | C2 |
| # reps | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 3 | 1 | 2 | 4 | 4 | 2 | 2 | 6 | 1 | 1 | 4 | 4 | 4 |
Matrix representation of C10.362+ 1+4 ►in GL8(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 35 | 35 | 0 | 0 | 0 | 0 |
| 0 | 0 | 6 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 40 |
| 32 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 9 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 38 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 1 | 1 | 13 |
| 0 | 0 | 0 | 0 | 28 | 26 | 13 | 13 |
| 0 | 0 | 0 | 0 | 3 | 25 | 11 | 17 |
| 0 | 0 | 0 | 0 | 16 | 25 | 5 | 11 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 22 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 30 | 40 | 0 |
| 0 | 0 | 0 | 0 | 1 | 7 | 0 | 40 |
| 9 | 29 | 0 | 0 | 0 | 0 | 0 | 0 |
| 34 | 32 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 23 | 38 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 27 | 13 | 1 |
| 0 | 0 | 0 | 0 | 28 | 26 | 13 | 13 |
| 0 | 0 | 0 | 0 | 3 | 19 | 17 | 11 |
| 0 | 0 | 0 | 0 | 16 | 19 | 11 | 5 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 34 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 26 | 20 | 14 |
| 0 | 0 | 0 | 0 | 9 | 21 | 27 | 21 |
G:=sub<GL(8,GF(41))| [40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,35,6,0,0,0,0,0,0,35,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[32,7,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,3,23,0,0,0,0,0,0,5,38,0,0,0,0,0,0,0,0,34,28,3,16,0,0,0,0,1,26,25,25,0,0,0,0,1,13,11,5,0,0,0,0,13,13,17,11],[1,22,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,1,30,7,0,0,0,0,0,0,40,0,0,0,0,0,0,0,0,40],[9,34,0,0,0,0,0,0,29,32,0,0,0,0,0,0,0,0,3,23,0,0,0,0,0,0,5,38,0,0,0,0,0,0,0,0,34,28,3,16,0,0,0,0,27,26,19,19,0,0,0,0,13,13,17,11,0,0,0,0,1,13,11,5],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,34,28,10,9,0,0,0,0,7,7,26,21,0,0,0,0,0,0,20,27,0,0,0,0,0,0,14,21] >;
C10.362+ 1+4 in GAP, Magma, Sage, TeX
C_{10}._{36}2_+^{1+4} % in TeX
G:=Group("C10.36ES+(2,2)"); // GroupNames label
G:=SmallGroup(320,1275);
// by ID
G=gap.SmallGroup(320,1275);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,219,675,570,297,12550]);
// Polycyclic
G:=Group<a,b,c,d,e|a^10=b^4=c^2=1,d^2=e^2=a^5*b^2,b*a*b^-1=d*a*d^-1=a^-1,a*c=c*a,a*e=e*a,c*b*c=a^5*b^-1,d*b*d^-1=a^5*b,b*e=e*b,d*c*d^-1=a^5*c,c*e=e*c,e*d*e^-1=a^5*b^2*d>;
// generators/relations