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G = C23.433C24  order 128 = 27

150th central stem extension by C23 of C24

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

Aliases: C23.433C24, C22.1722- 1+4, C42⋊5C4.9C2, C42⋊4C4.21C2, (C2×C42).62C22, (C22×C4).534C23, C23.65C23.50C2, C23.83C23.13C2, C23.63C23.26C2, C2.C42.177C22, C2.35(C22.50C24), C2.23(C22.35C24), C2.76(C23.36C23), C2.59(C22.46C24), (C4×C4⋊C4).61C2, (C2×C4).146(C4○D4), (C2×C4⋊C4).295C22, C22.310(C2×C4○D4), SmallGroup(128,1265)

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

Derived series
C1 — C23 — C23.433C24
Chief series
C1 — C2 — C22 — C23 — C22×C4 — C2×C42 — C4×C4⋊C4 — C23.433C24
Lower central
C1 — C23 — C23.433C24
Upper central
C1 — C23 — C23.433C24
Jennings
C1 — C23 — C23.433C24

Generators and relations for C23.433C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=ca=ac, e2=b, f2=a, g2=ba=ab, ede-1=gdg-1=ad=da, 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, eg=ge, fg=gf >

Subgroups: 292 in 182 conjugacy classes, 92 normal (82 characteristic)
C1, C2, C4, C22, C2×C4, C2×C4, C23, C42, C4⋊C4, C22×C4, C2.C42, C2×C42, C2×C4⋊C4, C42⋊4C4, C4×C4⋊C4, C42⋊5C4, C23.63C23, C23.65C23, C23.83C23, C23.433C24
Quotients: C1, C2, C22, C23, C4○D4, C24, C2×C4○D4, 2- 1+4, C23.36C23, C22.35C24, C22.46C24, C22.50C24, C23.433C24

Smallest permutation representation of C23.433C24
►Regular action on 128 points
Generators in S128
(1 77)(2 78)(3 79)(4 80)(5 127)(6 128)(7 125)(8 126)(9 39)(10 40)(11 37)(12 38)(13 20)(14 17)(15 18)(16 19)(21 28)(22 25)(23 26)(24 27)(29 36)(30 33)(31 34)(32 35)(41 46)(42 47)(43 48)(44 45)(49 54)(50 55)(51 56)(52 53)(57 62)(58 63)(59 64)(60 61)(65 70)(66 71)(67 72)(68 69)(73 97)(74 98)(75 99)(76 100)(81 86)(82 87)(83 88)(84 85)(89 94)(90 95)(91 96)(92 93)(101 108)(102 105)(103 106)(104 107)(109 116)(110 113)(111 114)(112 115)(117 124)(118 121)(119 122)(120 123)

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

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

(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)

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

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

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

38 conjugacy classes

class 1 2A···2G4A···4H4I···4Z4AA4AB4AC4AD
order12···24···44···44444
size11···12···24···48888

38 irreducible representations

dim111111124
type+++++++-
imageC1C2C2C2C2C2C2C4○D42- 1+4
kernelC23.433C24C42⋊4C4C4×C4⋊C4C42⋊5C4C23.63C23C23.65C23C23.83C23C2×C4C22
# reps1111624202

Matrix representation of C23.433C24 ►in GL6(𝔽5)

100000
010000
001000
000100
000040
000004
,
400000
040000
001000
000100
000010
000001
,
400000
040000
004000
000400
000010
000001
,
120000
440000
003000
000300
000002
000020
,
430000
110000
000300
002000
000002
000030
,
100000
440000
000100
001000
000030
000003
,
200000
020000
001000
000100
000001
000040

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],[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],[4,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,4,0,0,0,0,2,4,0,0,0,0,0,0,3,0,0,0,0,0,0,3,0,0,0,0,0,0,0,2,0,0,0,0,2,0],[4,1,0,0,0,0,3,1,0,0,0,0,0,0,0,2,0,0,0,0,3,0,0,0,0,0,0,0,0,3,0,0,0,0,2,0],[1,4,0,0,0,0,0,4,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,3,0,0,0,0,0,0,3],[2,0,0,0,0,0,0,2,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,0,1,0] >;
 

C23.433C24 in GAP, Magma, Sage, TeX 

C_2^3._{433}C_2^4
 
% in TeX
 
G:=Group("C2^3.433C2^4");
 
// GroupNames label
 
G:=SmallGroup(128,1265);
 
// by ID
 
G=gap.SmallGroup(128,1265);
 
# by ID
 
G:=PCGroup([7,-2,2,2,2,-2,2,2,560,253,232,758,723,100,675,192]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=1,d^2=c*a=a*c,e^2=b,f^2=a,g^2=b*a=a*b,e*d*e^-1=g*d*g^-1=a*d=d*a,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,e*g=g*e,f*g=g*f>;
 
// generators/relations
 

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