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G = C23.711C24  order 128 = 27

428th central stem extension by C23 of C24

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

Aliases: C23.711C24, C22.4842+ 1+4, C2.12Q82, (C2×Q8)⋊6Q8, (C22×C4).893C23, (C2×C42).729C22, C2.23(C23⋊2Q8), C22.171(C22×Q8), (C22×Q8).230C22, C2.14(C24⋊C22), C23.78C23.29C2, C23.67C23.63C2, C2.C42.415C22, (C2×C4).95(C2×Q8), (C2×C4⋊C4).521C22, SmallGroup(128,1543)

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

Derived series
C1 — C23 — C23.711C24
Chief series
C1 — C2 — C22 — C23 — C22×C4 — C2×C42 — C23.67C23 — C23.711C24
Lower central
C1 — C23 — C23.711C24
Upper central
C1 — C23 — C23.711C24
Jennings
C1 — C23 — C23.711C24

Generators and relations for C23.711C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=g2=ba=ab, e2=ca=ac, f2=cb=bc, ede-1=ad=da, geg-1=ae=ea, af=fa, ag=ga, 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: 420 in 216 conjugacy classes, 112 normal (5 characteristic)
C1, C2, C2, C4, C22, C22, C2×C4, C2×C4, Q8, C23, C42, C4⋊C4, C22×C4, C2×Q8, C2×Q8, C2.C42, C2×C42, C2×C4⋊C4, C22×Q8, C23.67C23, C23.78C23, C23.711C24
Quotients: C1, C2, C22, Q8, C23, C2×Q8, C24, C22×Q8, 2+ 1+4, C23⋊2Q8, Q82, C24⋊C22, C23.711C24

Smallest permutation representation of C23.711C24
►Regular action on 128 points
Generators in S128
(1 9)(2 10)(3 11)(4 12)(5 69)(6 70)(7 71)(8 72)(13 77)(14 78)(15 79)(16 80)(17 81)(18 82)(19 83)(20 84)(21 85)(22 86)(23 87)(24 88)(25 89)(26 90)(27 91)(28 92)(29 93)(30 94)(31 95)(32 96)(33 97)(34 98)(35 99)(36 100)(37 75)(38 76)(39 73)(40 74)(41 103)(42 104)(43 101)(44 102)(45 107)(46 108)(47 105)(48 106)(49 111)(50 112)(51 109)(52 110)(53 115)(54 116)(55 113)(56 114)(57 119)(58 120)(59 117)(60 118)(61 123)(62 124)(63 121)(64 122)(65 128)(66 125)(67 126)(68 127)

(1 11)(2 12)(3 9)(4 10)(5 71)(6 72)(7 69)(8 70)(13 79)(14 80)(15 77)(16 78)(17 83)(18 84)(19 81)(20 82)(21 87)(22 88)(23 85)(24 86)(25 91)(26 92)(27 89)(28 90)(29 95)(30 96)(31 93)(32 94)(33 99)(34 100)(35 97)(36 98)(37 73)(38 74)(39 75)(40 76)(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)(65 126)(66 127)(67 128)(68 125)

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

(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)

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

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

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

32 conjugacy classes

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

32 irreducible representations

dim11124
type+++-+
imageC1C2C2Q82+ 1+4
kernelC23.711C24C23.67C23C23.78C23C2×Q8C22
# reps196124

Matrix representation of C23.711C24 ►in GL6(𝔽5)

400000
040000
001000
000100
000010
000001
,
100000
010000
001000
000100
000040
000004
,
100000
010000
004000
000400
000010
000001
,
030000
300000
001000
000100
000020
000003
,
200000
030000
002200
000300
000010
000001
,
400000
040000
002000
001300
000001
000040
,
010000
400000
001000
000100
000001
000040

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

C23.711C24 in GAP, Magma, Sage, TeX 

C_2^3._{711}C_2^4
 
% in TeX
 
G:=Group("C2^3.711C2^4");
 
// GroupNames label
 
G:=SmallGroup(128,1543);
 
// by ID
 
G=gap.SmallGroup(128,1543);
 
# by ID
 
G:=PCGroup([7,-2,2,2,2,-2,2,2,336,253,568,758,723,520,1571,346,192]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=1,d^2=g^2=b*a=a*b,e^2=c*a=a*c,f^2=c*b=b*c,e*d*e^-1=a*d=d*a,g*e*g^-1=a*e=e*a,a*f=f*a,a*g=g*a,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
 

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