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G = C2×C22.58C24  order 128 = 27

Direct product of C2 and C22.58C24

direct product, p-group, metabelian, nilpotent (class 2), monomial, rational

Aliases: C2×C22.58C24, C22.119C25, C42.583C23, C23.280C24, C22.872- 1+4, C4⋊C4.308C23, (C2×C4).109C24, (C2×C42).963C22, C2.37(C2×2- 1+4), (C22×C4).1217C23, C42.C2.160C22, (C2×C4⋊C4).717C22, (C2×C42.C2).38C2, SmallGroup(128,2262)

Series: Derived ►Chief ►Lower central ►Upper central ►Jennings

Derived series
C1 — C22 — C2×C22.58C24
Chief series
C1 — C2 — C22 — C23 — C22×C4 — C2×C42 — C2×C42.C2 — C2×C22.58C24
Lower central
C1 — C22 — C2×C22.58C24
Upper central
C1 — C23 — C2×C22.58C24
Jennings
C1 — C22 — C2×C22.58C24

Generators and relations for C2×C22.58C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=g2=b, e2=f2=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, ede-1=bd=db, geg-1=be=eb, bf=fb, bg=gb, fdf-1=cd=dc, ce=ec, cf=fc, cg=gc, gdg-1=bcd, fef-1=bce, fg=gf >

Subgroups: 508 in 448 conjugacy classes, 388 normal (4 characteristic)
C1, C2, C4, C22, C22, C2×C4, C2×C4, C23, C42, C4⋊C4, C22×C4, C2×C42, C2×C4⋊C4, C42.C2, C2×C42.C2, C22.58C24, C2×C22.58C24
Quotients: C1, C2, C22, C23, C24, 2- 1+4, C25, C22.58C24, C2×2- 1+4, C2×C22.58C24

Smallest permutation representation of C2×C22.58C24
►Regular action on 128 points
Generators in S128
(1 97)(2 98)(3 99)(4 100)(5 36)(6 33)(7 34)(8 35)(9 103)(10 104)(11 101)(12 102)(13 127)(14 128)(15 125)(16 126)(17 111)(18 112)(19 109)(20 110)(21 107)(22 108)(23 105)(24 106)(25 119)(26 120)(27 117)(28 118)(29 115)(30 116)(31 113)(32 114)(37 123)(38 124)(39 121)(40 122)(41 75)(42 76)(43 73)(44 74)(45 67)(46 68)(47 65)(48 66)(49 83)(50 84)(51 81)(52 82)(53 79)(54 80)(55 77)(56 78)(57 91)(58 92)(59 89)(60 90)(61 87)(62 88)(63 85)(64 86)(69 96)(70 93)(71 94)(72 95)

(1 3)(2 4)(5 7)(6 8)(9 11)(10 12)(13 15)(14 16)(17 19)(18 20)(21 23)(22 24)(25 27)(26 28)(29 31)(30 32)(33 35)(34 36)(37 39)(38 40)(41 43)(42 44)(45 47)(46 48)(49 51)(50 52)(53 55)(54 56)(57 59)(58 60)(61 63)(62 64)(65 67)(66 68)(69 71)(70 72)(73 75)(74 76)(77 79)(78 80)(81 83)(82 84)(85 87)(86 88)(89 91)(90 92)(93 95)(94 96)(97 99)(98 100)(101 103)(102 104)(105 107)(106 108)(109 111)(110 112)(113 115)(114 116)(117 119)(118 120)(121 123)(122 124)(125 127)(126 128)

(1 35)(2 36)(3 33)(4 34)(5 98)(6 99)(7 100)(8 97)(9 45)(10 46)(11 47)(12 48)(13 72)(14 69)(15 70)(16 71)(17 53)(18 54)(19 55)(20 56)(21 41)(22 42)(23 43)(24 44)(25 61)(26 62)(27 63)(28 64)(29 49)(30 50)(31 51)(32 52)(37 57)(38 58)(39 59)(40 60)(65 101)(66 102)(67 103)(68 104)(73 105)(74 106)(75 107)(76 108)(77 109)(78 110)(79 111)(80 112)(81 113)(82 114)(83 115)(84 116)(85 117)(86 118)(87 119)(88 120)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)

(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)

(1 115 35 83)(2 114 36 82)(3 113 33 81)(4 116 34 84)(5 52 98 32)(6 51 99 31)(7 50 100 30)(8 49 97 29)(9 117 45 85)(10 120 46 88)(11 119 47 87)(12 118 48 86)(13 77 72 109)(14 80 69 112)(15 79 70 111)(16 78 71 110)(17 125 53 93)(18 128 54 96)(19 127 55 95)(20 126 56 94)(21 121 41 89)(22 124 42 92)(23 123 43 91)(24 122 44 90)(25 65 61 101)(26 68 62 104)(27 67 63 103)(28 66 64 102)(37 73 57 105)(38 76 58 108)(39 75 59 107)(40 74 60 106)

(1 107 35 75)(2 76 36 108)(3 105 33 73)(4 74 34 106)(5 22 98 42)(6 43 99 23)(7 24 100 44)(8 41 97 21)(9 109 45 77)(10 78 46 110)(11 111 47 79)(12 80 48 112)(13 119 72 87)(14 88 69 120)(15 117 70 85)(16 86 71 118)(17 65 53 101)(18 102 54 66)(19 67 55 103)(20 104 56 68)(25 95 61 127)(26 128 62 96)(27 93 63 125)(28 126 64 94)(29 91 49 123)(30 124 50 92)(31 89 51 121)(32 122 52 90)(37 115 57 83)(38 84 58 116)(39 113 59 81)(40 82 60 114)

(1 65 3 67)(2 104 4 102)(5 46 7 48)(6 9 8 11)(10 100 12 98)(13 91 15 89)(14 122 16 124)(17 73 19 75)(18 108 20 106)(21 79 23 77)(22 110 24 112)(25 83 27 81)(26 114 28 116)(29 85 31 87)(30 120 32 118)(33 103 35 101)(34 66 36 68)(37 93 39 95)(38 128 40 126)(41 111 43 109)(42 78 44 80)(45 97 47 99)(49 117 51 119)(50 88 52 86)(53 105 55 107)(54 76 56 74)(57 125 59 127)(58 96 60 94)(61 115 63 113)(62 82 64 84)(69 90 71 92)(70 121 72 123)
 
G:=sub<Sym(128)| (1,97)(2,98)(3,99)(4,100)(5,36)(6,33)(7,34)(8,35)(9,103)(10,104)(11,101)(12,102)(13,127)(14,128)(15,125)(16,126)(17,111)(18,112)(19,109)(20,110)(21,107)(22,108)(23,105)(24,106)(25,119)(26,120)(27,117)(28,118)(29,115)(30,116)(31,113)(32,114)(37,123)(38,124)(39,121)(40,122)(41,75)(42,76)(43,73)(44,74)(45,67)(46,68)(47,65)(48,66)(49,83)(50,84)(51,81)(52,82)(53,79)(54,80)(55,77)(56,78)(57,91)(58,92)(59,89)(60,90)(61,87)(62,88)(63,85)(64,86)(69,96)(70,93)(71,94)(72,95), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)(77,79)(78,80)(81,83)(82,84)(85,87)(86,88)(89,91)(90,92)(93,95)(94,96)(97,99)(98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128), (1,35)(2,36)(3,33)(4,34)(5,98)(6,99)(7,100)(8,97)(9,45)(10,46)(11,47)(12,48)(13,72)(14,69)(15,70)(16,71)(17,53)(18,54)(19,55)(20,56)(21,41)(22,42)(23,43)(24,44)(25,61)(26,62)(27,63)(28,64)(29,49)(30,50)(31,51)(32,52)(37,57)(38,58)(39,59)(40,60)(65,101)(66,102)(67,103)(68,104)(73,105)(74,106)(75,107)(76,108)(77,109)(78,110)(79,111)(80,112)(81,113)(82,114)(83,115)(84,116)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128), (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), (1,115,35,83)(2,114,36,82)(3,113,33,81)(4,116,34,84)(5,52,98,32)(6,51,99,31)(7,50,100,30)(8,49,97,29)(9,117,45,85)(10,120,46,88)(11,119,47,87)(12,118,48,86)(13,77,72,109)(14,80,69,112)(15,79,70,111)(16,78,71,110)(17,125,53,93)(18,128,54,96)(19,127,55,95)(20,126,56,94)(21,121,41,89)(22,124,42,92)(23,123,43,91)(24,122,44,90)(25,65,61,101)(26,68,62,104)(27,67,63,103)(28,66,64,102)(37,73,57,105)(38,76,58,108)(39,75,59,107)(40,74,60,106), (1,107,35,75)(2,76,36,108)(3,105,33,73)(4,74,34,106)(5,22,98,42)(6,43,99,23)(7,24,100,44)(8,41,97,21)(9,109,45,77)(10,78,46,110)(11,111,47,79)(12,80,48,112)(13,119,72,87)(14,88,69,120)(15,117,70,85)(16,86,71,118)(17,65,53,101)(18,102,54,66)(19,67,55,103)(20,104,56,68)(25,95,61,127)(26,128,62,96)(27,93,63,125)(28,126,64,94)(29,91,49,123)(30,124,50,92)(31,89,51,121)(32,122,52,90)(37,115,57,83)(38,84,58,116)(39,113,59,81)(40,82,60,114), (1,65,3,67)(2,104,4,102)(5,46,7,48)(6,9,8,11)(10,100,12,98)(13,91,15,89)(14,122,16,124)(17,73,19,75)(18,108,20,106)(21,79,23,77)(22,110,24,112)(25,83,27,81)(26,114,28,116)(29,85,31,87)(30,120,32,118)(33,103,35,101)(34,66,36,68)(37,93,39,95)(38,128,40,126)(41,111,43,109)(42,78,44,80)(45,97,47,99)(49,117,51,119)(50,88,52,86)(53,105,55,107)(54,76,56,74)(57,125,59,127)(58,96,60,94)(61,115,63,113)(62,82,64,84)(69,90,71,92)(70,121,72,123)>;
 
G:=Group( (1,97)(2,98)(3,99)(4,100)(5,36)(6,33)(7,34)(8,35)(9,103)(10,104)(11,101)(12,102)(13,127)(14,128)(15,125)(16,126)(17,111)(18,112)(19,109)(20,110)(21,107)(22,108)(23,105)(24,106)(25,119)(26,120)(27,117)(28,118)(29,115)(30,116)(31,113)(32,114)(37,123)(38,124)(39,121)(40,122)(41,75)(42,76)(43,73)(44,74)(45,67)(46,68)(47,65)(48,66)(49,83)(50,84)(51,81)(52,82)(53,79)(54,80)(55,77)(56,78)(57,91)(58,92)(59,89)(60,90)(61,87)(62,88)(63,85)(64,86)(69,96)(70,93)(71,94)(72,95), (1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36)(37,39)(38,40)(41,43)(42,44)(45,47)(46,48)(49,51)(50,52)(53,55)(54,56)(57,59)(58,60)(61,63)(62,64)(65,67)(66,68)(69,71)(70,72)(73,75)(74,76)(77,79)(78,80)(81,83)(82,84)(85,87)(86,88)(89,91)(90,92)(93,95)(94,96)(97,99)(98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128), (1,35)(2,36)(3,33)(4,34)(5,98)(6,99)(7,100)(8,97)(9,45)(10,46)(11,47)(12,48)(13,72)(14,69)(15,70)(16,71)(17,53)(18,54)(19,55)(20,56)(21,41)(22,42)(23,43)(24,44)(25,61)(26,62)(27,63)(28,64)(29,49)(30,50)(31,51)(32,52)(37,57)(38,58)(39,59)(40,60)(65,101)(66,102)(67,103)(68,104)(73,105)(74,106)(75,107)(76,108)(77,109)(78,110)(79,111)(80,112)(81,113)(82,114)(83,115)(84,116)(85,117)(86,118)(87,119)(88,120)(89,121)(90,122)(91,123)(92,124)(93,125)(94,126)(95,127)(96,128), (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), (1,115,35,83)(2,114,36,82)(3,113,33,81)(4,116,34,84)(5,52,98,32)(6,51,99,31)(7,50,100,30)(8,49,97,29)(9,117,45,85)(10,120,46,88)(11,119,47,87)(12,118,48,86)(13,77,72,109)(14,80,69,112)(15,79,70,111)(16,78,71,110)(17,125,53,93)(18,128,54,96)(19,127,55,95)(20,126,56,94)(21,121,41,89)(22,124,42,92)(23,123,43,91)(24,122,44,90)(25,65,61,101)(26,68,62,104)(27,67,63,103)(28,66,64,102)(37,73,57,105)(38,76,58,108)(39,75,59,107)(40,74,60,106), (1,107,35,75)(2,76,36,108)(3,105,33,73)(4,74,34,106)(5,22,98,42)(6,43,99,23)(7,24,100,44)(8,41,97,21)(9,109,45,77)(10,78,46,110)(11,111,47,79)(12,80,48,112)(13,119,72,87)(14,88,69,120)(15,117,70,85)(16,86,71,118)(17,65,53,101)(18,102,54,66)(19,67,55,103)(20,104,56,68)(25,95,61,127)(26,128,62,96)(27,93,63,125)(28,126,64,94)(29,91,49,123)(30,124,50,92)(31,89,51,121)(32,122,52,90)(37,115,57,83)(38,84,58,116)(39,113,59,81)(40,82,60,114), (1,65,3,67)(2,104,4,102)(5,46,7,48)(6,9,8,11)(10,100,12,98)(13,91,15,89)(14,122,16,124)(17,73,19,75)(18,108,20,106)(21,79,23,77)(22,110,24,112)(25,83,27,81)(26,114,28,116)(29,85,31,87)(30,120,32,118)(33,103,35,101)(34,66,36,68)(37,93,39,95)(38,128,40,126)(41,111,43,109)(42,78,44,80)(45,97,47,99)(49,117,51,119)(50,88,52,86)(53,105,55,107)(54,76,56,74)(57,125,59,127)(58,96,60,94)(61,115,63,113)(62,82,64,84)(69,90,71,92)(70,121,72,123) );
 
G=PermutationGroup([[(1,97),(2,98),(3,99),(4,100),(5,36),(6,33),(7,34),(8,35),(9,103),(10,104),(11,101),(12,102),(13,127),(14,128),(15,125),(16,126),(17,111),(18,112),(19,109),(20,110),(21,107),(22,108),(23,105),(24,106),(25,119),(26,120),(27,117),(28,118),(29,115),(30,116),(31,113),(32,114),(37,123),(38,124),(39,121),(40,122),(41,75),(42,76),(43,73),(44,74),(45,67),(46,68),(47,65),(48,66),(49,83),(50,84),(51,81),(52,82),(53,79),(54,80),(55,77),(56,78),(57,91),(58,92),(59,89),(60,90),(61,87),(62,88),(63,85),(64,86),(69,96),(70,93),(71,94),(72,95)], [(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20),(21,23),(22,24),(25,27),(26,28),(29,31),(30,32),(33,35),(34,36),(37,39),(38,40),(41,43),(42,44),(45,47),(46,48),(49,51),(50,52),(53,55),(54,56),(57,59),(58,60),(61,63),(62,64),(65,67),(66,68),(69,71),(70,72),(73,75),(74,76),(77,79),(78,80),(81,83),(82,84),(85,87),(86,88),(89,91),(90,92),(93,95),(94,96),(97,99),(98,100),(101,103),(102,104),(105,107),(106,108),(109,111),(110,112),(113,115),(114,116),(117,119),(118,120),(121,123),(122,124),(125,127),(126,128)], [(1,35),(2,36),(3,33),(4,34),(5,98),(6,99),(7,100),(8,97),(9,45),(10,46),(11,47),(12,48),(13,72),(14,69),(15,70),(16,71),(17,53),(18,54),(19,55),(20,56),(21,41),(22,42),(23,43),(24,44),(25,61),(26,62),(27,63),(28,64),(29,49),(30,50),(31,51),(32,52),(37,57),(38,58),(39,59),(40,60),(65,101),(66,102),(67,103),(68,104),(73,105),(74,106),(75,107),(76,108),(77,109),(78,110),(79,111),(80,112),(81,113),(82,114),(83,115),(84,116),(85,117),(86,118),(87,119),(88,120),(89,121),(90,122),(91,123),(92,124),(93,125),(94,126),(95,127),(96,128)], [(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)], [(1,115,35,83),(2,114,36,82),(3,113,33,81),(4,116,34,84),(5,52,98,32),(6,51,99,31),(7,50,100,30),(8,49,97,29),(9,117,45,85),(10,120,46,88),(11,119,47,87),(12,118,48,86),(13,77,72,109),(14,80,69,112),(15,79,70,111),(16,78,71,110),(17,125,53,93),(18,128,54,96),(19,127,55,95),(20,126,56,94),(21,121,41,89),(22,124,42,92),(23,123,43,91),(24,122,44,90),(25,65,61,101),(26,68,62,104),(27,67,63,103),(28,66,64,102),(37,73,57,105),(38,76,58,108),(39,75,59,107),(40,74,60,106)], [(1,107,35,75),(2,76,36,108),(3,105,33,73),(4,74,34,106),(5,22,98,42),(6,43,99,23),(7,24,100,44),(8,41,97,21),(9,109,45,77),(10,78,46,110),(11,111,47,79),(12,80,48,112),(13,119,72,87),(14,88,69,120),(15,117,70,85),(16,86,71,118),(17,65,53,101),(18,102,54,66),(19,67,55,103),(20,104,56,68),(25,95,61,127),(26,128,62,96),(27,93,63,125),(28,126,64,94),(29,91,49,123),(30,124,50,92),(31,89,51,121),(32,122,52,90),(37,115,57,83),(38,84,58,116),(39,113,59,81),(40,82,60,114)], [(1,65,3,67),(2,104,4,102),(5,46,7,48),(6,9,8,11),(10,100,12,98),(13,91,15,89),(14,122,16,124),(17,73,19,75),(18,108,20,106),(21,79,23,77),(22,110,24,112),(25,83,27,81),(26,114,28,116),(29,85,31,87),(30,120,32,118),(33,103,35,101),(34,66,36,68),(37,93,39,95),(38,128,40,126),(41,111,43,109),(42,78,44,80),(45,97,47,99),(49,117,51,119),(50,88,52,86),(53,105,55,107),(54,76,56,74),(57,125,59,127),(58,96,60,94),(61,115,63,113),(62,82,64,84),(69,90,71,92),(70,121,72,123)]])
 

38 conjugacy classes

class 1 2A···2G4A···4AD
order12···24···4
size11···14···4

38 irreducible representations

dim1114
type+++-
imageC1C2C22- 1+4
kernelC2×C22.58C24C2×C42.C2C22.58C24C22
# reps115166

Matrix representation of C2×C22.58C24 ►in GL12(𝔽5)

400000000000
040000000000
004000000000
000400000000
000010000000
000001000000
000000100000
000000010000
000000004000
000000000400
000000000040
000000000004
,
100000000000
010000000000
001000000000
000100000000
000010000000
000001000000
000000100000
000000010000
000000004000
000000000400
000000000040
000000000004
,
400000000000
040000000000
004000000000
000400000000
000040000000
000004000000
000000400000
000000040000
000000001000
000000000100
000000000010
000000000001
,
442100000000
344100000000
401300000000
034100000000
000002340000
000022040000
000021210000
000042110000
000000000020
000000003234
000000002000
000000002023
,
100300000000
143000000000
011400000000
100400000000
000040020000
000002000000
000041330000
000040010000
000000000020
000000003234
000000003000
000000000323
,
001000000000
231000000000
400000000000
031200000000
000040200000
000022200000
000040100000
000004330000
000000000010
000000001413
000000001000
000000000001
,
130000000000
040000000000
144000000000
133100000000
000042000000
000001000000
000023100000
000003040000
000000000100
000000004000
000000001413
000000001014

G:=sub<GL(12,GF(5))| [4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4],[4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1],[4,3,4,0,0,0,0,0,0,0,0,0,4,4,0,3,0,0,0,0,0,0,0,0,2,4,1,4,0,0,0,0,0,0,0,0,1,1,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,4,0,0,0,0,0,0,0,0,2,2,1,2,0,0,0,0,0,0,0,0,3,0,2,1,0,0,0,0,0,0,0,0,4,4,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,3,2,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,2,3,0,2,0,0,0,0,0,0,0,0,0,4,0,3],[1,1,0,1,0,0,0,0,0,0,0,0,0,4,1,0,0,0,0,0,0,0,0,0,0,3,1,0,0,0,0,0,0,0,0,0,3,0,4,4,0,0,0,0,0,0,0,0,0,0,0,0,4,0,4,4,0,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,2,0,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,3,3,0,0,0,0,0,0,0,0,0,0,2,0,3,0,0,0,0,0,0,0,0,2,3,0,2,0,0,0,0,0,0,0,0,0,4,0,3],[0,2,4,0,0,0,0,0,0,0,0,0,0,3,0,3,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,4,2,4,0,0,0,0,0,0,0,0,0,0,2,0,4,0,0,0,0,0,0,0,0,2,2,1,3,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,3,0,1],[1,0,1,1,0,0,0,0,0,0,0,0,3,4,4,3,0,0,0,0,0,0,0,0,0,0,4,3,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,4,0,2,0,0,0,0,0,0,0,0,0,2,1,3,3,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,4,1,1,0,0,0,0,0,0,0,0,1,0,4,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,3,4] >;
 

C2×C22.58C24 in GAP, Magma, Sage, TeX 

C_2\times C_2^2._{58}C_2^4
 
% in TeX
 
G:=Group("C2xC2^2.58C2^4");
 
// GroupNames label
 
G:=SmallGroup(128,2262);
 
// by ID
 
G=gap.SmallGroup(128,2262);
 
# by ID
 
G:=PCGroup([7,-2,2,2,2,2,-2,2,224,477,456,1430,1059,352,2915,570,136]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=1,d^2=g^2=b,e^2=f^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,e*d*e^-1=b*d=d*b,g*e*g^-1=b*e=e*b,b*f=f*b,b*g=g*b,f*d*f^-1=c*d=d*c,c*e=e*c,c*f=f*c,c*g=g*c,g*d*g^-1=b*c*d,f*e*f^-1=b*c*e,f*g=g*f>;
 
// generators/relations
 

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