Copied to
clipboard

G = C24.634C23order 128 = 27

13rd central extension by C24 of C23

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

Aliases: C24.634C23, (C22xC4).9Q8, C22.37(C4xQ8), C22.127(C4xD4), C23.724(C2xD4), (C22xC4).125D4, C22.24(C4:Q8), C23.133(C2xQ8), C2.C42:13C4, C2.3(C42:9C4), C22.70C22wrC2, C2.3(C23:2D4), (C23xC4).12C22, C23.347(C4oD4), C22.25(C4:1D4), C23.303(C22xC4), C22.64(C22:Q8), C2.2(C23.4Q8), C2.6(C23.8Q8), C22.103(C4:D4), C22.22(C42.C2), C2.6(C23.65C23), C2.3(C23.81C23), C2.2(C23.78C23), C22.76(C22.D4), (C2xC4):4(C4:C4), (C22xC4:C4).5C2, C22.79(C2xC4:C4), (C22xC4).170(C2xC4), (C2xC2.C42).13C2, SmallGroup(128,176)

Series: Derived Chief Lower central Upper central Jennings

C1C23 — C24.634C23
C1C2C22C23C24C23xC4C2xC2.C42 — C24.634C23
C1C23 — C24.634C23
C1C24 — C24.634C23
C1C24 — C24.634C23

Generators and relations for C24.634C23
 G = < a,b,c,d,e,f,g | a2=b2=c2=d2=1, e2=d, f2=a, g2=b, 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: 532 in 304 conjugacy classes, 124 normal (13 characteristic)
C1, C2, C2, C4, C22, C22, C2xC4, C2xC4, C23, C23, C4:C4, C22xC4, C22xC4, C24, C2.C42, C2.C42, C2xC4:C4, C23xC4, C23xC4, C2xC2.C42, C2xC2.C42, C22xC4:C4, C24.634C23
Quotients: C1, C2, C4, C22, C2xC4, D4, Q8, C23, C4:C4, C22xC4, C2xD4, C2xQ8, C4oD4, C2xC4:C4, C4xD4, C4xQ8, C22wrC2, C4:D4, C22:Q8, C22.D4, C42.C2, C4:1D4, C4:Q8, C42:9C4, C23.8Q8, C23.65C23, C23:2D4, C23.78C23, C23.81C23, C23.4Q8, C24.634C23

Smallest permutation representation of C24.634C23
Regular action on 128 points
Generators in S128
(1 75)(2 76)(3 73)(4 74)(5 34)(6 35)(7 36)(8 33)(9 13)(10 14)(11 15)(12 16)(17 21)(18 22)(19 23)(20 24)(25 29)(26 30)(27 31)(28 32)(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)(69 93)(70 94)(71 95)(72 96)(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 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 91 75 87)(2 88 76 92)(3 89 73 85)(4 86 74 90)(5 18 34 22)(6 23 35 19)(7 20 36 24)(8 21 33 17)(9 29 13 25)(10 26 14 30)(11 31 15 27)(12 28 16 32)(37 57 41 53)(38 54 42 58)(39 59 43 55)(40 56 44 60)(45 67 49 61)(46 62 50 68)(47 65 51 63)(48 64 52 66)(69 81 93 77)(70 78 94 82)(71 83 95 79)(72 80 96 84)(97 117 101 113)(98 114 102 118)(99 119 103 115)(100 116 104 120)(105 125 109 121)(106 122 110 126)(107 127 111 123)(108 124 112 128)
(1 19 11 79)(2 80 12 20)(3 17 9 77)(4 78 10 18)(5 118 70 58)(6 59 71 119)(7 120 72 60)(8 57 69 117)(13 81 73 21)(14 22 74 82)(15 83 75 23)(16 24 76 84)(25 121 85 61)(26 62 86 122)(27 123 87 63)(28 64 88 124)(29 125 89 67)(30 68 90 126)(31 127 91 65)(32 66 92 128)(33 53 93 113)(34 114 94 54)(35 55 95 115)(36 116 96 56)(37 105 97 45)(38 46 98 106)(39 107 99 47)(40 48 100 108)(41 109 101 49)(42 50 102 110)(43 111 103 51)(44 52 104 112)

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

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

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

44 conjugacy classes

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

44 irreducible representations

dim1111222
type++++-
imageC1C2C2C4D4Q8C4oD4
kernelC24.634C23C2xC2.C42C22xC4:C4C2.C42C22xC4C22xC4C23
# reps14381288

Matrix representation of C24.634C23 in GL8(F5)

40000000
04000000
00400000
00040000
00004000
00000400
00000040
00000004
,
40000000
04000000
00400000
00040000
00004000
00000400
00000010
00000001
,
10000000
01000000
00400000
00040000
00004000
00000400
00000010
00000001
,
10000000
01000000
00100000
00010000
00004000
00000400
00000040
00000004
,
01000000
10000000
00400000
00210000
00002100
00000300
00000030
00000032
,
20000000
03000000
00440000
00210000
00001300
00001400
00000013
00000014
,
30000000
02000000
00330000
00020000
00002000
00002300
00000010
00000001

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

C24.634C23 in GAP, Magma, Sage, TeX

C_2^4._{634}C_2^3
% in TeX

G:=Group("C2^4.634C2^3");
// GroupNames label

G:=SmallGroup(128,176);
// by ID

G=gap.SmallGroup(128,176);
# by ID

G:=PCGroup([7,-2,2,2,-2,2,2,2,448,141,64,422,387,100]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=1,e^2=d,f^2=a,g^2=b,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

׿
x
:
Z
F
o
wr
Q
<