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G = C23.711C24order 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(C232Q8), 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

C1C23 — C23.711C24
C1C2C22C23C22×C4C2×C42C23.67C23 — C23.711C24
C1C23 — C23.711C24
C1C23 — C23.711C24
C1C23 — 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 [×6], C4 [×24], C22, C22 [×6], C2×C4 [×18], C2×C4 [×36], Q8 [×20], C23, C42 [×3], C4⋊C4 [×9], C22×C4 [×15], C2×Q8 [×12], C2×Q8 [×12], C2.C42 [×18], C2×C42 [×3], C2×C4⋊C4 [×9], C22×Q8 [×5], C23.67C23 [×9], C23.78C23 [×6], C23.711C24
Quotients: C1, C2 [×15], C22 [×35], Q8 [×12], C23 [×15], C2×Q8 [×18], C24, C22×Q8 [×3], 2+ 1+4 [×4], C232Q8 [×3], Q82 [×3], C24⋊C22, C23.711C24

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

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

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

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

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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