p-group, metabelian, nilpotent (class 2), monomial
Aliases: C24.632C23, (C22×C4).7Q8, C22.35(C4×Q8), (C22×C4).123D4, C22.125(C4×D4), C23.722(C2×D4), C22.23(C4⋊Q8), C23.131(C2×Q8), C2.C42⋊12C4, C2.4(C42⋊8C4), C22.69C22≀C2, (C23×C4).10C22, C2.2(C23⋊Q8), C23.345(C4○D4), C23.301(C22×C4), C22.62(C22⋊Q8), C2.5(C23.8Q8), C22.101(C4⋊D4), C22.51(C4.4D4), C2.3(C23.11D4), C2.5(C23.10D4), C22.20(C42.C2), C22.75(C42⋊C2), C22.26(C42⋊2C2), C2.7(C24.C22), C2.2(C23.81C23), C2.2(C23.83C23), C2.5(C23.63C23), C2.5(C23.65C23), C22.74(C22.D4), (C2×C4).32(C4⋊C4), (C22×C4⋊C4).4C2, C22.78(C2×C4⋊C4), (C22×C4).99(C2×C4), (C2×C2.C42).5C2, SmallGroup(128,174)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C24.632C23
G = < a,b,c,d,e,f,g | a2=b2=c2=d2=1, e2=d, f2=b, g2=a, 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: 484 in 260 conjugacy classes, 108 normal (34 characteristic)
C1, C2, C2, C4, C22, C22, C2×C4, C2×C4, C23, C23, C4⋊C4, C22×C4, C22×C4, C24, C2.C42, C2.C42, C2×C4⋊C4, C23×C4, C23×C4, C2×C2.C42, C2×C2.C42, C22×C4⋊C4, C24.632C23
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, C2×C4⋊C4, C42⋊C2, C4×D4, C4×Q8, C22≀C2, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42.C2, C42⋊2C2, C4⋊Q8, C42⋊8C4, C23.8Q8, C23.63C23, C24.C22, C23.65C23, C23⋊Q8, C23.10D4, C23.11D4, C23.81C23, C23.83C23, C24.632C23
►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 25 9 85)(2 30 10 90)(3 27 11 87)(4 32 12 92)(5 80 70 20)(6 81 71 21)(7 78 72 18)(8 83 69 23)(13 89 73 29)(14 86 74 26)(15 91 75 31)(16 88 76 28)(17 93 77 33)(19 95 79 35)(22 94 82 34)(24 96 84 36)(37 113 97 53)(38 118 98 58)(39 115 99 55)(40 120 100 60)(41 117 101 57)(42 114 102 54)(43 119 103 59)(44 116 104 56)(45 121 105 61)(46 126 106 68)(47 123 107 63)(48 128 108 66)(49 125 109 67)(50 122 110 62)(51 127 111 65)(52 124 112 64)
(1 81 73 77)(2 22 74 18)(3 83 75 79)(4 24 76 20)(5 58 96 54)(6 119 93 115)(7 60 94 56)(8 117 95 113)(9 21 13 17)(10 82 14 78)(11 23 15 19)(12 84 16 80)(25 65 29 63)(26 128 30 124)(27 67 31 61)(28 126 32 122)(33 55 71 59)(34 116 72 120)(35 53 69 57)(36 114 70 118)(37 49 41 45)(38 110 42 106)(39 51 43 47)(40 112 44 108)(46 98 50 102)(48 100 52 104)(62 88 68 92)(64 86 66 90)(85 127 89 123)(87 125 91 121)(97 109 101 105)(99 111 103 107)
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), (1,25,9,85)(2,30,10,90)(3,27,11,87)(4,32,12,92)(5,80,70,20)(6,81,71,21)(7,78,72,18)(8,83,69,23)(13,89,73,29)(14,86,74,26)(15,91,75,31)(16,88,76,28)(17,93,77,33)(19,95,79,35)(22,94,82,34)(24,96,84,36)(37,113,97,53)(38,118,98,58)(39,115,99,55)(40,120,100,60)(41,117,101,57)(42,114,102,54)(43,119,103,59)(44,116,104,56)(45,121,105,61)(46,126,106,68)(47,123,107,63)(48,128,108,66)(49,125,109,67)(50,122,110,62)(51,127,111,65)(52,124,112,64), (1,81,73,77)(2,22,74,18)(3,83,75,79)(4,24,76,20)(5,58,96,54)(6,119,93,115)(7,60,94,56)(8,117,95,113)(9,21,13,17)(10,82,14,78)(11,23,15,19)(12,84,16,80)(25,65,29,63)(26,128,30,124)(27,67,31,61)(28,126,32,122)(33,55,71,59)(34,116,72,120)(35,53,69,57)(36,114,70,118)(37,49,41,45)(38,110,42,106)(39,51,43,47)(40,112,44,108)(46,98,50,102)(48,100,52,104)(62,88,68,92)(64,86,66,90)(85,127,89,123)(87,125,91,121)(97,109,101,105)(99,111,103,107)>;
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), (1,25,9,85)(2,30,10,90)(3,27,11,87)(4,32,12,92)(5,80,70,20)(6,81,71,21)(7,78,72,18)(8,83,69,23)(13,89,73,29)(14,86,74,26)(15,91,75,31)(16,88,76,28)(17,93,77,33)(19,95,79,35)(22,94,82,34)(24,96,84,36)(37,113,97,53)(38,118,98,58)(39,115,99,55)(40,120,100,60)(41,117,101,57)(42,114,102,54)(43,119,103,59)(44,116,104,56)(45,121,105,61)(46,126,106,68)(47,123,107,63)(48,128,108,66)(49,125,109,67)(50,122,110,62)(51,127,111,65)(52,124,112,64), (1,81,73,77)(2,22,74,18)(3,83,75,79)(4,24,76,20)(5,58,96,54)(6,119,93,115)(7,60,94,56)(8,117,95,113)(9,21,13,17)(10,82,14,78)(11,23,15,19)(12,84,16,80)(25,65,29,63)(26,128,30,124)(27,67,31,61)(28,126,32,122)(33,55,71,59)(34,116,72,120)(35,53,69,57)(36,114,70,118)(37,49,41,45)(38,110,42,106)(39,51,43,47)(40,112,44,108)(46,98,50,102)(48,100,52,104)(62,88,68,92)(64,86,66,90)(85,127,89,123)(87,125,91,121)(97,109,101,105)(99,111,103,107) );
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)], [(1,25,9,85),(2,30,10,90),(3,27,11,87),(4,32,12,92),(5,80,70,20),(6,81,71,21),(7,78,72,18),(8,83,69,23),(13,89,73,29),(14,86,74,26),(15,91,75,31),(16,88,76,28),(17,93,77,33),(19,95,79,35),(22,94,82,34),(24,96,84,36),(37,113,97,53),(38,118,98,58),(39,115,99,55),(40,120,100,60),(41,117,101,57),(42,114,102,54),(43,119,103,59),(44,116,104,56),(45,121,105,61),(46,126,106,68),(47,123,107,63),(48,128,108,66),(49,125,109,67),(50,122,110,62),(51,127,111,65),(52,124,112,64)], [(1,81,73,77),(2,22,74,18),(3,83,75,79),(4,24,76,20),(5,58,96,54),(6,119,93,115),(7,60,94,56),(8,117,95,113),(9,21,13,17),(10,82,14,78),(11,23,15,19),(12,84,16,80),(25,65,29,63),(26,128,30,124),(27,67,31,61),(28,126,32,122),(33,55,71,59),(34,116,72,120),(35,53,69,57),(36,114,70,118),(37,49,41,45),(38,110,42,106),(39,51,43,47),(40,112,44,108),(46,98,50,102),(48,100,52,104),(62,88,68,92),(64,86,66,90),(85,127,89,123),(87,125,91,121),(97,109,101,105),(99,111,103,107)]])
44 conjugacy classes
| class | 1 | 2A | ··· | 2O | 4A | ··· | 4AB |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 |
| size | 1 | 1 | ··· | 1 | 4 | ··· | 4 |
44 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C4 | D4 | Q8 | C4○D4 |
| kernel | C24.632C23 | C2×C2.C42 | C22×C4⋊C4 | C2.C42 | C22×C4 | C22×C4 | C23 |
| # reps | 1 | 6 | 1 | 8 | 8 | 4 | 16 |
Matrix representation of C24.632C23 ►in GL7(𝔽5)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 2 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 3 | 0 |
| 0 | 0 | 0 | 0 | 0 | 2 | 2 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 4 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 2 | 0 |
| 0 | 0 | 0 | 0 | 0 | 3 | 3 |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 4 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 2 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 4 | 3 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
G:=sub<GL(7,GF(5))| [1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4],[4,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4],[2,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,3,0,0,0,0,0,0,0,3,2,0,0,0,0,0,0,2],[1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,3,4,0,0,0,0,0,0,0,4,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,2,3,0,0,0,0,0,0,3],[4,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,4,0,0,0,0,0,0,3,1] >;
C24.632C23 in GAP, Magma, Sage, TeX
C_2^4._{632}C_2^3 % in TeX
G:=Group("C2^4.632C2^3"); // GroupNames label
G:=SmallGroup(128,174);
// by ID
G=gap.SmallGroup(128,174);
# by ID
G:=PCGroup([7,-2,2,2,-2,2,2,2,448,141,120,422,387,58]);
// Polycyclic
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=1,e^2=d,f^2=b,g^2=a,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