metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22.F5⋊4C4, (C22×C4).3F5, C22.3(C4×F5), (C22×C20).9C4, C22.4(C4⋊F5), C23.35(C2×F5), Dic5.8(C4⋊C4), (C2×C10).15C42, (C2×Dic5).12Q8, C2.2(C23.F5), C5⋊2(C22.C42), (C2×Dic5).104D4, C10.2(C4.D4), (C22×Dic5).8C4, C10.5(C4.10D4), Dic5.6(C22⋊C4), C22.40(C22⋊F5), C2.19(D10.3Q8), C2.3(Dic5.D4), C10.19(C2.C42), (C22×Dic5).174C22, (C2×C10).18(C4⋊C4), (C2×C22.F5).2C2, (C22×C10).48(C2×C4), (C2×Dic5).45(C2×C4), (C2×C10.D4).2C2, (C2×C10).32(C22⋊C4), SmallGroup(320,257)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C22.F5⋊C4
G = < a,b,c,d,e | a2=b2=c4=d5=1, e4=b, eae-1=ab=ba, ac=ca, ad=da, bc=cb, bd=db, be=eb, cd=dc, ece-1=abc, ede-1=d3 >
Subgroups: 354 in 98 conjugacy classes, 38 normal (24 characteristic)
C1, C2, C2, C4, C22, C22, C5, C8, C2×C4, C23, C10, C10, C4⋊C4, C2×C8, M4(2), C22×C4, C22×C4, Dic5, Dic5, C20, C2×C10, C2×C10, C2×C4⋊C4, C2×M4(2), C5⋊C8, C2×Dic5, C2×Dic5, C2×Dic5, C2×C20, C22×C10, C22.C42, C10.D4, C2×C5⋊C8, C22.F5, C22.F5, C22×Dic5, C22×C20, C2×C10.D4, C2×C22.F5, C22.F5⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C42, C22⋊C4, C4⋊C4, F5, C2.C42, C4.D4, C4.10D4, C2×F5, C22.C42, C4×F5, C4⋊F5, C22⋊F5, Dic5.D4, D10.3Q8, C23.F5, C22.F5⋊C4
►On 160 points
Generators in S160
(1 88)(2 85)(3 82)(4 87)(5 84)(6 81)(7 86)(8 83)(9 137)(10 142)(11 139)(12 144)(13 141)(14 138)(15 143)(16 140)(17 151)(18 148)(19 145)(20 150)(21 147)(22 152)(23 149)(24 146)(25 134)(26 131)(27 136)(28 133)(29 130)(30 135)(31 132)(32 129)(33 52)(34 49)(35 54)(36 51)(37 56)(38 53)(39 50)(40 55)(41 113)(42 118)(43 115)(44 120)(45 117)(46 114)(47 119)(48 116)(57 71)(58 68)(59 65)(60 70)(61 67)(62 72)(63 69)(64 66)(73 95)(74 92)(75 89)(76 94)(77 91)(78 96)(79 93)(80 90)(97 154)(98 159)(99 156)(100 153)(101 158)(102 155)(103 160)(104 157)(105 121)(106 126)(107 123)(108 128)(109 125)(110 122)(111 127)(112 124)
(1 5)(2 6)(3 7)(4 8)(9 13)(10 14)(11 15)(12 16)(17 21)(18 22)(19 23)(20 24)(25 29)(26 30)(27 31)(28 32)(33 37)(34 38)(35 39)(36 40)(41 45)(42 46)(43 47)(44 48)(49 53)(50 54)(51 55)(52 56)(57 61)(58 62)(59 63)(60 64)(65 69)(66 70)(67 71)(68 72)(73 77)(74 78)(75 79)(76 80)(81 85)(82 86)(83 87)(84 88)(89 93)(90 94)(91 95)(92 96)(97 101)(98 102)(99 103)(100 104)(105 109)(106 110)(107 111)(108 112)(113 117)(114 118)(115 119)(116 120)(121 125)(122 126)(123 127)(124 128)(129 133)(130 134)(131 135)(132 136)(137 141)(138 142)(139 143)(140 144)(145 149)(146 150)(147 151)(148 152)(153 157)(154 158)(155 159)(156 160)
(1 78 88 96)(2 93 81 75)(3 76 82 94)(4 91 83 73)(5 74 84 92)(6 89 85 79)(7 80 86 90)(8 95 87 77)(9 31 137 132)(10 129 138 28)(11 29 139 130)(12 135 140 26)(13 27 141 136)(14 133 142 32)(15 25 143 134)(16 131 144 30)(17 60 147 66)(18 67 148 61)(19 58 149 72)(20 65 150 59)(21 64 151 70)(22 71 152 57)(23 62 145 68)(24 69 146 63)(33 125 56 105)(34 106 49 126)(35 123 50 111)(36 112 51 124)(37 121 52 109)(38 110 53 122)(39 127 54 107)(40 108 55 128)(41 104 113 157)(42 154 114 101)(43 102 115 155)(44 160 116 99)(45 100 117 153)(46 158 118 97)(47 98 119 159)(48 156 120 103)
(1 159 15 40 65)(2 33 160 66 16)(3 67 34 9 153)(4 10 68 154 35)(5 155 11 36 69)(6 37 156 70 12)(7 71 38 13 157)(8 14 72 158 39)(17 131 93 125 116)(18 126 132 117 94)(19 118 127 95 133)(20 96 119 134 128)(21 135 89 121 120)(22 122 136 113 90)(23 114 123 91 129)(24 92 115 130 124)(25 108 150 78 47)(26 79 109 48 151)(27 41 80 152 110)(28 145 42 111 73)(29 112 146 74 43)(30 75 105 44 147)(31 45 76 148 106)(32 149 46 107 77)(49 137 100 82 61)(50 83 138 62 101)(51 63 84 102 139)(52 103 64 140 85)(53 141 104 86 57)(54 87 142 58 97)(55 59 88 98 143)(56 99 60 144 81)
(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)
G:=sub<Sym(160)| (1,88)(2,85)(3,82)(4,87)(5,84)(6,81)(7,86)(8,83)(9,137)(10,142)(11,139)(12,144)(13,141)(14,138)(15,143)(16,140)(17,151)(18,148)(19,145)(20,150)(21,147)(22,152)(23,149)(24,146)(25,134)(26,131)(27,136)(28,133)(29,130)(30,135)(31,132)(32,129)(33,52)(34,49)(35,54)(36,51)(37,56)(38,53)(39,50)(40,55)(41,113)(42,118)(43,115)(44,120)(45,117)(46,114)(47,119)(48,116)(57,71)(58,68)(59,65)(60,70)(61,67)(62,72)(63,69)(64,66)(73,95)(74,92)(75,89)(76,94)(77,91)(78,96)(79,93)(80,90)(97,154)(98,159)(99,156)(100,153)(101,158)(102,155)(103,160)(104,157)(105,121)(106,126)(107,123)(108,128)(109,125)(110,122)(111,127)(112,124), (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64)(65,69)(66,70)(67,71)(68,72)(73,77)(74,78)(75,79)(76,80)(81,85)(82,86)(83,87)(84,88)(89,93)(90,94)(91,95)(92,96)(97,101)(98,102)(99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160), (1,78,88,96)(2,93,81,75)(3,76,82,94)(4,91,83,73)(5,74,84,92)(6,89,85,79)(7,80,86,90)(8,95,87,77)(9,31,137,132)(10,129,138,28)(11,29,139,130)(12,135,140,26)(13,27,141,136)(14,133,142,32)(15,25,143,134)(16,131,144,30)(17,60,147,66)(18,67,148,61)(19,58,149,72)(20,65,150,59)(21,64,151,70)(22,71,152,57)(23,62,145,68)(24,69,146,63)(33,125,56,105)(34,106,49,126)(35,123,50,111)(36,112,51,124)(37,121,52,109)(38,110,53,122)(39,127,54,107)(40,108,55,128)(41,104,113,157)(42,154,114,101)(43,102,115,155)(44,160,116,99)(45,100,117,153)(46,158,118,97)(47,98,119,159)(48,156,120,103), (1,159,15,40,65)(2,33,160,66,16)(3,67,34,9,153)(4,10,68,154,35)(5,155,11,36,69)(6,37,156,70,12)(7,71,38,13,157)(8,14,72,158,39)(17,131,93,125,116)(18,126,132,117,94)(19,118,127,95,133)(20,96,119,134,128)(21,135,89,121,120)(22,122,136,113,90)(23,114,123,91,129)(24,92,115,130,124)(25,108,150,78,47)(26,79,109,48,151)(27,41,80,152,110)(28,145,42,111,73)(29,112,146,74,43)(30,75,105,44,147)(31,45,76,148,106)(32,149,46,107,77)(49,137,100,82,61)(50,83,138,62,101)(51,63,84,102,139)(52,103,64,140,85)(53,141,104,86,57)(54,87,142,58,97)(55,59,88,98,143)(56,99,60,144,81), (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)>;
G:=Group( (1,88)(2,85)(3,82)(4,87)(5,84)(6,81)(7,86)(8,83)(9,137)(10,142)(11,139)(12,144)(13,141)(14,138)(15,143)(16,140)(17,151)(18,148)(19,145)(20,150)(21,147)(22,152)(23,149)(24,146)(25,134)(26,131)(27,136)(28,133)(29,130)(30,135)(31,132)(32,129)(33,52)(34,49)(35,54)(36,51)(37,56)(38,53)(39,50)(40,55)(41,113)(42,118)(43,115)(44,120)(45,117)(46,114)(47,119)(48,116)(57,71)(58,68)(59,65)(60,70)(61,67)(62,72)(63,69)(64,66)(73,95)(74,92)(75,89)(76,94)(77,91)(78,96)(79,93)(80,90)(97,154)(98,159)(99,156)(100,153)(101,158)(102,155)(103,160)(104,157)(105,121)(106,126)(107,123)(108,128)(109,125)(110,122)(111,127)(112,124), (1,5)(2,6)(3,7)(4,8)(9,13)(10,14)(11,15)(12,16)(17,21)(18,22)(19,23)(20,24)(25,29)(26,30)(27,31)(28,32)(33,37)(34,38)(35,39)(36,40)(41,45)(42,46)(43,47)(44,48)(49,53)(50,54)(51,55)(52,56)(57,61)(58,62)(59,63)(60,64)(65,69)(66,70)(67,71)(68,72)(73,77)(74,78)(75,79)(76,80)(81,85)(82,86)(83,87)(84,88)(89,93)(90,94)(91,95)(92,96)(97,101)(98,102)(99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160), (1,78,88,96)(2,93,81,75)(3,76,82,94)(4,91,83,73)(5,74,84,92)(6,89,85,79)(7,80,86,90)(8,95,87,77)(9,31,137,132)(10,129,138,28)(11,29,139,130)(12,135,140,26)(13,27,141,136)(14,133,142,32)(15,25,143,134)(16,131,144,30)(17,60,147,66)(18,67,148,61)(19,58,149,72)(20,65,150,59)(21,64,151,70)(22,71,152,57)(23,62,145,68)(24,69,146,63)(33,125,56,105)(34,106,49,126)(35,123,50,111)(36,112,51,124)(37,121,52,109)(38,110,53,122)(39,127,54,107)(40,108,55,128)(41,104,113,157)(42,154,114,101)(43,102,115,155)(44,160,116,99)(45,100,117,153)(46,158,118,97)(47,98,119,159)(48,156,120,103), (1,159,15,40,65)(2,33,160,66,16)(3,67,34,9,153)(4,10,68,154,35)(5,155,11,36,69)(6,37,156,70,12)(7,71,38,13,157)(8,14,72,158,39)(17,131,93,125,116)(18,126,132,117,94)(19,118,127,95,133)(20,96,119,134,128)(21,135,89,121,120)(22,122,136,113,90)(23,114,123,91,129)(24,92,115,130,124)(25,108,150,78,47)(26,79,109,48,151)(27,41,80,152,110)(28,145,42,111,73)(29,112,146,74,43)(30,75,105,44,147)(31,45,76,148,106)(32,149,46,107,77)(49,137,100,82,61)(50,83,138,62,101)(51,63,84,102,139)(52,103,64,140,85)(53,141,104,86,57)(54,87,142,58,97)(55,59,88,98,143)(56,99,60,144,81), (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) );
G=PermutationGroup([[(1,88),(2,85),(3,82),(4,87),(5,84),(6,81),(7,86),(8,83),(9,137),(10,142),(11,139),(12,144),(13,141),(14,138),(15,143),(16,140),(17,151),(18,148),(19,145),(20,150),(21,147),(22,152),(23,149),(24,146),(25,134),(26,131),(27,136),(28,133),(29,130),(30,135),(31,132),(32,129),(33,52),(34,49),(35,54),(36,51),(37,56),(38,53),(39,50),(40,55),(41,113),(42,118),(43,115),(44,120),(45,117),(46,114),(47,119),(48,116),(57,71),(58,68),(59,65),(60,70),(61,67),(62,72),(63,69),(64,66),(73,95),(74,92),(75,89),(76,94),(77,91),(78,96),(79,93),(80,90),(97,154),(98,159),(99,156),(100,153),(101,158),(102,155),(103,160),(104,157),(105,121),(106,126),(107,123),(108,128),(109,125),(110,122),(111,127),(112,124)], [(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16),(17,21),(18,22),(19,23),(20,24),(25,29),(26,30),(27,31),(28,32),(33,37),(34,38),(35,39),(36,40),(41,45),(42,46),(43,47),(44,48),(49,53),(50,54),(51,55),(52,56),(57,61),(58,62),(59,63),(60,64),(65,69),(66,70),(67,71),(68,72),(73,77),(74,78),(75,79),(76,80),(81,85),(82,86),(83,87),(84,88),(89,93),(90,94),(91,95),(92,96),(97,101),(98,102),(99,103),(100,104),(105,109),(106,110),(107,111),(108,112),(113,117),(114,118),(115,119),(116,120),(121,125),(122,126),(123,127),(124,128),(129,133),(130,134),(131,135),(132,136),(137,141),(138,142),(139,143),(140,144),(145,149),(146,150),(147,151),(148,152),(153,157),(154,158),(155,159),(156,160)], [(1,78,88,96),(2,93,81,75),(3,76,82,94),(4,91,83,73),(5,74,84,92),(6,89,85,79),(7,80,86,90),(8,95,87,77),(9,31,137,132),(10,129,138,28),(11,29,139,130),(12,135,140,26),(13,27,141,136),(14,133,142,32),(15,25,143,134),(16,131,144,30),(17,60,147,66),(18,67,148,61),(19,58,149,72),(20,65,150,59),(21,64,151,70),(22,71,152,57),(23,62,145,68),(24,69,146,63),(33,125,56,105),(34,106,49,126),(35,123,50,111),(36,112,51,124),(37,121,52,109),(38,110,53,122),(39,127,54,107),(40,108,55,128),(41,104,113,157),(42,154,114,101),(43,102,115,155),(44,160,116,99),(45,100,117,153),(46,158,118,97),(47,98,119,159),(48,156,120,103)], [(1,159,15,40,65),(2,33,160,66,16),(3,67,34,9,153),(4,10,68,154,35),(5,155,11,36,69),(6,37,156,70,12),(7,71,38,13,157),(8,14,72,158,39),(17,131,93,125,116),(18,126,132,117,94),(19,118,127,95,133),(20,96,119,134,128),(21,135,89,121,120),(22,122,136,113,90),(23,114,123,91,129),(24,92,115,130,124),(25,108,150,78,47),(26,79,109,48,151),(27,41,80,152,110),(28,145,42,111,73),(29,112,146,74,43),(30,75,105,44,147),(31,45,76,148,106),(32,149,46,107,77),(49,137,100,82,61),(50,83,138,62,101),(51,63,84,102,139),(52,103,64,140,85),(53,141,104,86,57),(54,87,142,58,97),(55,59,88,98,143),(56,99,60,144,81)], [(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)]])
38 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 5 | 8A | ··· | 8H | 10A | ··· | 10G | 20A | ··· | 20H |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 8 | ··· | 8 | 10 | ··· | 10 | 20 | ··· | 20 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 10 | 10 | 10 | 10 | 20 | 20 | 4 | 20 | ··· | 20 | 4 | ··· | 4 | 4 | ··· | 4 |
38 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | + | + | - | ||||||
| image | C1 | C2 | C2 | C4 | C4 | C4 | D4 | Q8 | F5 | C4.D4 | C4.10D4 | C2×F5 | C4×F5 | C4⋊F5 | C22⋊F5 | Dic5.D4 | C23.F5 |
| kernel | C22.F5⋊C4 | C2×C10.D4 | C2×C22.F5 | C22.F5 | C22×Dic5 | C22×C20 | C2×Dic5 | C2×Dic5 | C22×C4 | C10 | C10 | C23 | C22 | C22 | C22 | C2 | C2 |
| # reps | 1 | 1 | 2 | 8 | 2 | 2 | 3 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 4 | 4 |
Matrix representation of C22.F5⋊C4 ►in GL6(𝔽41)
| 40 | 0 | 0 | 0 | 0 | 0 |
| 0 | 40 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 40 | 0 | 0 | 0 |
| 0 | 0 | 0 | 40 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 25 | 18 | 0 | 0 | 0 | 0 |
| 29 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 38 | 32 | 0 | 0 |
| 0 | 0 | 33 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 9 |
| 0 | 0 | 0 | 0 | 8 | 38 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 31 | 1 | 0 | 0 |
| 0 | 0 | 10 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 34 |
| 0 | 0 | 0 | 0 | 12 | 19 |
| 13 | 13 | 0 | 0 | 0 | 0 |
| 9 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 40 | 0 |
| 0 | 0 | 0 | 0 | 0 | 40 |
| 0 | 0 | 14 | 9 | 0 | 0 |
| 0 | 0 | 10 | 27 | 0 | 0 |
G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[25,29,0,0,0,0,18,16,0,0,0,0,0,0,38,33,0,0,0,0,32,3,0,0,0,0,0,0,3,8,0,0,0,0,9,38],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,31,10,0,0,0,0,1,3,0,0,0,0,0,0,28,12,0,0,0,0,34,19],[13,9,0,0,0,0,13,28,0,0,0,0,0,0,0,0,14,10,0,0,0,0,9,27,0,0,40,0,0,0,0,0,0,40,0,0] >;
C22.F5⋊C4 in GAP, Magma, Sage, TeX
C_2^2.F_5\rtimes C_4
% in TeX
G:=Group("C2^2.F5:C4"); // GroupNames label
G:=SmallGroup(320,257);
// by ID
G=gap.SmallGroup(320,257);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,28,253,64,387,184,1684,6278,3156]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^4=d^5=1,e^4=b,e*a*e^-1=a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,e*c*e^-1=a*b*c,e*d*e^-1=d^3>;
// generators/relations