Copied to
clipboard

G = C2xC23.83C23order 128 = 27

Direct product of C2 and C23.83C23

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

Aliases: C2xC23.83C23, C24.651C23, C23.294C24, (C22xC4).56Q8, (C22xC4).369D4, C23.835(C2xD4), C23.146(C2xQ8), (C23xC4).67C22, C23.372(C4oD4), C22.59(C22xQ8), (C22xC4).497C23, C22.177(C22xD4), C22.95(C22:Q8), C22.79(C4.4D4), C22.28(C42.C2), C22.34(C42:2C2), C2.C42.484C22, C22.105(C22.D4), (C2xC4).295(C2xD4), (C2xC4).121(C2xQ8), C2.9(C2xC4.4D4), C2.12(C2xC22:Q8), C2.6(C2xC42.C2), (C22xC4:C4).32C2, C2.7(C2xC42:2C2), (C2xC4:C4).837C22, C22.174(C2xC4oD4), C2.11(C2xC22.D4), (C2xC2.C42).24C2, SmallGroup(128,1126)

Series: Derived Chief Lower central Upper central Jennings

C1C23 — C2xC23.83C23
C1C2C22C23C24C23xC4C2xC2.C42 — C2xC23.83C23
C1C23 — C2xC23.83C23
C1C24 — C2xC23.83C23
C1C23 — C2xC23.83C23

Generators and relations for C2xC23.83C23
 G = < a,b,c,d,e,f,g | a2=b2=c2=d2=1, e2=g2=b, f2=cb=bc, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bd=db, fef-1=be=eb, bf=fb, bg=gb, cd=dc, geg-1=ce=ec, cf=fc, cg=gc, de=ed, gfg-1=df=fd, dg=gd >

Subgroups: 516 in 302 conjugacy classes, 148 normal (16 characteristic)
C1, C2, C2, C4, C22, C22, C2xC4, C2xC4, C23, C23, C4:C4, C22xC4, C22xC4, C24, C2.C42, C2xC4:C4, C2xC4:C4, C23xC4, C23xC4, C2xC2.C42, C2xC2.C42, C23.83C23, C22xC4:C4, C2xC23.83C23
Quotients: C1, C2, C22, D4, Q8, C23, C2xD4, C2xQ8, C4oD4, C24, C22:Q8, C22.D4, C4.4D4, C42.C2, C42:2C2, C22xD4, C22xQ8, C2xC4oD4, C23.83C23, C2xC22:Q8, C2xC22.D4, C2xC4.4D4, C2xC42.C2, C2xC42:2C2, C2xC23.83C23

Smallest permutation representation of C2xC23.83C23
Regular action on 128 points
Generators in S128
(1 33)(2 34)(3 35)(4 36)(5 46)(6 47)(7 48)(8 45)(9 103)(10 104)(11 101)(12 102)(13 107)(14 108)(15 105)(16 106)(17 119)(18 120)(19 117)(20 118)(21 123)(22 124)(23 121)(24 122)(25 111)(26 112)(27 109)(28 110)(29 115)(30 116)(31 113)(32 114)(37 65)(38 66)(39 67)(40 68)(41 127)(42 128)(43 125)(44 126)(49 85)(50 86)(51 87)(52 88)(53 89)(54 90)(55 91)(56 92)(57 69)(58 70)(59 71)(60 72)(61 81)(62 82)(63 83)(64 84)(73 96)(74 93)(75 94)(76 95)(77 100)(78 97)(79 98)(80 99)
(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 9)(2 10)(3 11)(4 12)(5 79)(6 80)(7 77)(8 78)(13 65)(14 66)(15 67)(16 68)(17 85)(18 86)(19 87)(20 88)(21 89)(22 90)(23 91)(24 92)(25 69)(26 70)(27 71)(28 72)(29 81)(30 82)(31 83)(32 84)(33 103)(34 104)(35 101)(36 102)(37 107)(38 108)(39 105)(40 106)(41 93)(42 94)(43 95)(44 96)(45 97)(46 98)(47 99)(48 100)(49 119)(50 120)(51 117)(52 118)(53 123)(54 124)(55 121)(56 122)(57 111)(58 112)(59 109)(60 110)(61 115)(62 116)(63 113)(64 114)(73 126)(74 127)(75 128)(76 125)
(1 105)(2 106)(3 107)(4 108)(5 96)(6 93)(7 94)(8 95)(9 39)(10 40)(11 37)(12 38)(13 35)(14 36)(15 33)(16 34)(17 55)(18 56)(19 53)(20 54)(21 51)(22 52)(23 49)(24 50)(25 63)(26 64)(27 61)(28 62)(29 59)(30 60)(31 57)(32 58)(41 80)(42 77)(43 78)(44 79)(45 76)(46 73)(47 74)(48 75)(65 101)(66 102)(67 103)(68 104)(69 113)(70 114)(71 115)(72 116)(81 109)(82 110)(83 111)(84 112)(85 121)(86 122)(87 123)(88 124)(89 117)(90 118)(91 119)(92 120)(97 125)(98 126)(99 127)(100 128)
(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 23 11 89)(2 22 12 92)(3 21 9 91)(4 24 10 90)(5 110 77 58)(6 109 78 57)(7 112 79 60)(8 111 80 59)(13 87 67 17)(14 86 68 20)(15 85 65 19)(16 88 66 18)(25 99 71 45)(26 98 72 48)(27 97 69 47)(28 100 70 46)(29 95 83 41)(30 94 84 44)(31 93 81 43)(32 96 82 42)(33 121 101 53)(34 124 102 56)(35 123 103 55)(36 122 104 54)(37 117 105 49)(38 120 106 52)(39 119 107 51)(40 118 108 50)(61 125 113 74)(62 128 114 73)(63 127 115 76)(64 126 116 75)
(1 83 3 81)(2 32 4 30)(5 24 7 22)(6 89 8 91)(9 31 11 29)(10 84 12 82)(13 27 15 25)(14 72 16 70)(17 74 19 76)(18 128 20 126)(21 78 23 80)(26 66 28 68)(33 63 35 61)(34 114 36 116)(37 59 39 57)(38 110 40 112)(41 51 43 49)(42 118 44 120)(45 55 47 53)(46 122 48 124)(50 94 52 96)(54 98 56 100)(58 108 60 106)(62 104 64 102)(65 71 67 69)(73 86 75 88)(77 90 79 92)(85 127 87 125)(93 117 95 119)(97 121 99 123)(101 115 103 113)(105 111 107 109)

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

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

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

44 conjugacy classes

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

44 irreducible representations

dim1111222
type+++++-
imageC1C2C2C2D4Q8C4oD4
kernelC2xC23.83C23C2xC2.C42C23.83C23C22xC4:C4C22xC4C22xC4C23
# reps15824420

Matrix representation of C2xC23.83C23 in GL8(F5)

10000000
01000000
00100000
00010000
00004000
00000400
00000040
00000004
,
40000000
04000000
00100000
00010000
00004000
00000400
00000040
00000004
,
10000000
01000000
00100000
00010000
00001000
00000100
00000040
00000004
,
10000000
01000000
00400000
00040000
00004000
00000400
00000040
00000004
,
03000000
30000000
00100000
00010000
00000400
00001000
00000030
00000002
,
04000000
10000000
00100000
00240000
00000300
00003000
00000001
00000010
,
30000000
03000000
00320000
00120000
00000400
00001000
00000001
00000040

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

C2xC23.83C23 in GAP, Magma, Sage, TeX

C_2\times C_2^3._{83}C_2^3
% in TeX

G:=Group("C2xC2^3.83C2^3");
// GroupNames label

G:=SmallGroup(128,1126);
// by ID

G=gap.SmallGroup(128,1126);
# by ID

G:=PCGroup([7,-2,2,2,2,-2,2,2,112,253,344,758,723,100]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=1,e^2=g^2=b,f^2=c*b=b*c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,b*d=d*b,f*e*f^-1=b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,g*e*g^-1=c*e=e*c,c*f=f*c,c*g=g*c,d*e=e*d,g*f*g^-1=d*f=f*d,d*g=g*d>;
// generators/relations

׿
x
:
Z
F
o
wr
Q
<