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G = C24.636C23  order 128 = 27

15th central extension by C24 of C23

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

Aliases: C24.636C23, (C22×C4)⋊2Q8, (C22×Q8)⋊12C4, (Q8×C23).1C2, C22.39(C4×Q8), C23.726(C2×D4), (C22×C4).197D4, C22.26(C4⋊Q8), C23.135(C2×Q8), C2.4(C24⋊3C4), C22.71C22≀C2, (C23×C4).14C22, C2.3(C23⋊Q8), C23.349(C4○D4), C23.305(C22×C4), C22.66(C22⋊Q8), C22.54(C4.4D4), C2.3(C23.78C23), C2.6(C23.67C23), (C2×C4).67(C22⋊C4), (C22×C4).171(C2×C4), C22.143(C2×C22⋊C4), (C2×C2.C42).15C2, SmallGroup(128,178)

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

Derived series
C1 — C23 — C24.636C23
Chief series
C1 — C2 — C22 — C23 — C24 — C23×C4 — Q8×C23 — C24.636C23
Lower central
C1 — C23 — C24.636C23
Upper central
C1 — C24 — C24.636C23
Jennings
C1 — C24 — C24.636C23

Generators and relations for C24.636C23
 G = < a,b,c,d,e,f,g | a2=b2=c2=d2=1, e2=d, f2=g2=c, ab=ba, ac=ca, ad=da, fef-1=ae=ea, af=fa, ag=ga, bc=cb, bd=db, geg-1=be=eb, bf=fb, bg=gb, cd=dc, ce=ec, gfg-1=cf=fc, cg=gc, de=ed, df=fd, dg=gd >

Subgroups: 660 in 368 conjugacy classes, 124 normal (6 characteristic)
C1, C2, C2, C4, C22, C2×C4, C2×C4, Q8, C23, C23, C22×C4, C22×C4, C2×Q8, C24, C2.C42, C23×C4, C22×Q8, C22×Q8, C2×C2.C42, Q8×C23, C24.636C23
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, C22⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, C2×C22⋊C4, C4×Q8, C22≀C2, C22⋊Q8, C4.4D4, C4⋊Q8, C24⋊3C4, C23.67C23, C23⋊Q8, C23.78C23, C24.636C23

Smallest permutation representation of C24.636C23
►Regular action on 128 points
Generators in S128
(1 73)(2 74)(3 75)(4 76)(5 96)(6 93)(7 94)(8 95)(9 13)(10 14)(11 15)(12 16)(17 21)(18 22)(19 23)(20 24)(25 29)(26 30)(27 31)(28 32)(33 71)(34 72)(35 69)(36 70)(37 41)(38 42)(39 43)(40 44)(45 49)(46 50)(47 51)(48 52)(53 57)(54 58)(55 59)(56 60)(61 67)(62 68)(63 65)(64 66)(77 81)(78 82)(79 83)(80 84)(85 89)(86 90)(87 91)(88 92)(97 101)(98 102)(99 103)(100 104)(105 109)(106 110)(107 111)(108 112)(113 117)(114 118)(115 119)(116 120)(121 125)(122 126)(123 127)(124 128)

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

(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)

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

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

44 conjugacy classes

class 1 2A···2O4A···4AB
order12···24···4
size11···14···4

44 irreducible representations

dim1111222
type++++-
imageC1C2C2C4D4Q8C4○D4
kernelC24.636C23C2×C2.C42Q8×C23C22×Q8C22×C4C22×C4C23
# reps16181288

Matrix representation of C24.636C23 ►in GL8(𝔽5)

40000000
04000000
00100000
00010000
00001000
00000100
00000040
00000004
,
10000000
01000000
00400000
00040000
00004000
00000400
00000040
00000004
,
10000000
01000000
00400000
00040000
00004000
00000400
00000010
00000001
,
10000000
01000000
00400000
00040000
00001000
00000100
00000010
00000001
,
40000000
21000000
00040000
00100000
00003200
00001200
00000003
00000020
,
44000000
01000000
00010000
00400000
00001400
00002400
00000001
00000010
,
40000000
04000000
00300000
00020000
00003200
00000200
00000001
00000010

G:=sub<GL(8,GF(5))| [4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[4,2,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,3,1,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,3,0],[4,0,0,0,0,0,0,0,4,1,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;
 

C24.636C23 in GAP, Magma, Sage, TeX 

C_2^4._{636}C_2^3
 
% in TeX
 
G:=Group("C2^4.636C2^3");
 
// GroupNames label
 
G:=SmallGroup(128,178);
 
// by ID
 
G=gap.SmallGroup(128,178);
 
# by ID
 
G:=PCGroup([7,-2,2,2,-2,2,2,2,448,141,232,422,387,184]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=1,e^2=d,f^2=g^2=c,a*b=b*a,a*c=c*a,a*d=d*a,f*e*f^-1=a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,b*d=d*b,g*e*g^-1=b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,c*e=e*c,g*f*g^-1=c*f=f*c,c*g=g*c,d*e=e*d,d*f=f*d,d*g=g*d>;
 
// generators/relations
 

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