Copied to
clipboard

G = C23.694C24  order 128 = 27

411st central stem extension by C23 of C24

p-group, metabelian, nilpotent (class 2), monomial

Aliases: C23.694C24, C22.3572- 1+4, C22.4672+ 1+4, C42⋊9C4.39C2, (C2×C42).110C22, (C22×C4).604C23, C23.81C23.45C2, C23.83C23.41C2, C23.63C23.55C2, C2.C42.398C22, C2.53(C22.57C24), C2.42(C22.53C24), C2.61(C22.35C24), C2.112(C22.33C24), C2.121(C22.46C24), (C2×C4).235(C4○D4), (C2×C4⋊C4).504C22, C22.555(C2×C4○D4), SmallGroup(128,1526)

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

Derived series
C1 — C23 — C23.694C24
Chief series
C1 — C2 — C22 — C23 — C22×C4 — C2×C42 — C23.63C23 — C23.694C24
Lower central
C1 — C23 — C23.694C24
Upper central
C1 — C23 — C23.694C24
Jennings
C1 — C23 — C23.694C24

Generators and relations for C23.694C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=c, e2=g2=ba=ab, f2=b, ac=ca, ede-1=ad=da, geg-1=ae=ea, af=fa, ag=ga, bc=cb, fdf-1=bd=db, be=eb, bf=fb, bg=gb, cd=dc, fef-1=ce=ec, cf=fc, cg=gc, gdg-1=abd, fg=gf >

Subgroups: 292 in 172 conjugacy classes, 88 normal (22 characteristic)
C1, C2, C2, C4, C22, C22, C2×C4, C2×C4, C23, C42, C4⋊C4, C22×C4, C22×C4, C2.C42, C2.C42, C2×C42, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C42⋊9C4, C23.63C23, C23.81C23, C23.83C23, C23.83C23, C23.694C24
Quotients: C1, C2, C22, C23, C4○D4, C24, C2×C4○D4, 2+ 1+4, 2- 1+4, C22.33C24, C22.35C24, C22.46C24, C22.53C24, C22.57C24, C23.694C24

Smallest permutation representation of C23.694C24
►Regular action on 128 points
Generators in S128
(1 11)(2 12)(3 9)(4 10)(5 70)(6 71)(7 72)(8 69)(13 73)(14 74)(15 75)(16 76)(17 77)(18 78)(19 79)(20 80)(21 81)(22 82)(23 83)(24 84)(25 85)(26 86)(27 87)(28 88)(29 89)(30 90)(31 91)(32 92)(33 93)(34 94)(35 95)(36 96)(37 97)(38 98)(39 99)(40 100)(41 101)(42 102)(43 103)(44 104)(45 105)(46 106)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 113)(54 114)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(61 121)(62 122)(63 123)(64 124)(65 127)(66 128)(67 125)(68 126)

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

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

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

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

32 conjugacy classes

class 1 2A···2G4A···4R4S···4X
order12···24···44···4
size11···14···48···8

32 irreducible representations

dim11111244
type++++++-
imageC1C2C2C2C2C4○D42+ 1+42- 1+4
kernelC23.694C24C42⋊9C4C23.63C23C23.81C23C23.83C23C2×C4C22C22
# reps118151213

Matrix representation of C23.694C24 ►in GL6(𝔽5)

100000
010000
001000
000100
000040
000004
,
100000
010000
004000
000400
000010
000001
,
400000
040000
001000
000100
000010
000001
,
200000
020000
003400
003200
000010
000044
,
020000
300000
002000
000200
000024
000003
,
010000
100000
003000
003200
000010
000001
,
100000
010000
003000
003200
000012
000044

G:=sub<GL(6,GF(5))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[4,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[2,0,0,0,0,0,0,2,0,0,0,0,0,0,3,3,0,0,0,0,4,2,0,0,0,0,0,0,1,4,0,0,0,0,0,4],[0,3,0,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,2,0,0,0,0,0,0,2,0,0,0,0,0,4,3],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,3,3,0,0,0,0,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,3,3,0,0,0,0,0,2,0,0,0,0,0,0,1,4,0,0,0,0,2,4] >;
 

C23.694C24 in GAP, Magma, Sage, TeX 

C_2^3._{694}C_2^4
 
% in TeX
 
G:=Group("C2^3.694C2^4");
 
// GroupNames label
 
G:=SmallGroup(128,1526);
 
// by ID
 
G=gap.SmallGroup(128,1526);
 
# by ID
 
G:=PCGroup([7,-2,2,2,2,-2,2,2,448,253,344,758,723,184,1571,346,192]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=1,d^2=c,e^2=g^2=b*a=a*b,f^2=b,a*c=c*a,e*d*e^-1=a*d=d*a,g*e*g^-1=a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,f*d*f^-1=b*d=d*b,b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,f*e*f^-1=c*e=e*c,c*f=f*c,c*g=g*c,g*d*g^-1=a*b*d,f*g=g*f>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁