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G = C23.488C24order 128 = 27

205th central stem extension by C23 of C24

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

Aliases: C23.488C24, C22.2002- 1+4, C22.2702+ 1+4, C4⋊C423Q8, C2.46(D43Q8), C2.24(Q83Q8), (C2×C42).581C22, (C22×C4).114C23, C22.123(C22×Q8), (C22×Q8).145C22, C2.61(C22.45C24), C23.65C23.63C2, C2.C42.222C22, C23.81C23.22C2, C23.78C23.12C2, C23.67C23.46C2, C23.83C23.19C2, C23.63C23.32C2, C2.32(C22.33C24), C2.46(C22.50C24), C2.34(C23.37C23), C2.92(C23.36C23), (C4×C4⋊C4).74C2, (C2×C4).64(C2×Q8), (C2×C4).527(C4○D4), (C2×C4⋊C4).879C22, C22.364(C2×C4○D4), SmallGroup(128,1320)

Series: Derived Chief Lower central Upper central Jennings

C1C23 — C23.488C24
C1C2C22C23C22×C4C2×C42C4×C4⋊C4 — C23.488C24
C1C23 — C23.488C24
C1C23 — C23.488C24
C1C23 — C23.488C24

Generators and relations for C23.488C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=a, e2=abc, f2=c, g2=b, ab=ba, ac=ca, 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: 324 in 194 conjugacy classes, 100 normal (82 characteristic)
C1, C2 [×7], C4 [×22], C22 [×7], C2×C4 [×14], C2×C4 [×38], Q8 [×4], C23, C42 [×7], C4⋊C4 [×4], C4⋊C4 [×18], C22×C4 [×15], C2×Q8 [×5], C2.C42 [×18], C2×C42 [×5], C2×C4⋊C4 [×11], C22×Q8, C4×C4⋊C4 [×2], C23.63C23 [×6], C23.65C23, C23.67C23 [×2], C23.78C23, C23.81C23, C23.83C23 [×2], C23.488C24
Quotients: C1, C2 [×15], C22 [×35], Q8 [×4], C23 [×15], C2×Q8 [×6], C4○D4 [×8], C24, C22×Q8, C2×C4○D4 [×4], 2+ 1+4, 2- 1+4, C23.36C23, C23.37C23, C22.33C24, C22.45C24, D43Q8, C22.50C24, Q83Q8, C23.488C24

Smallest permutation representation of C23.488C24
Regular action on 128 points
Generators in S128
(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 71)(6 72)(7 69)(8 70)(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)(41 103)(42 104)(43 101)(44 102)(45 107)(46 108)(47 105)(48 106)(49 111)(50 112)(51 109)(52 110)(53 115)(54 116)(55 113)(56 114)(57 119)(58 120)(59 117)(60 118)(61 123)(62 124)(63 121)(64 122)(65 126)(66 127)(67 128)(68 125)
(1 101)(2 102)(3 103)(4 104)(5 100)(6 97)(7 98)(8 99)(9 43)(10 44)(11 41)(12 42)(13 47)(14 48)(15 45)(16 46)(17 51)(18 52)(19 49)(20 50)(21 55)(22 56)(23 53)(24 54)(25 59)(26 60)(27 57)(28 58)(29 63)(30 64)(31 61)(32 62)(33 68)(34 65)(35 66)(36 67)(37 72)(38 69)(39 70)(40 71)(73 105)(74 106)(75 107)(76 108)(77 109)(78 110)(79 111)(80 112)(81 113)(82 114)(83 115)(84 116)(85 117)(86 118)(87 119)(88 120)(89 121)(90 122)(91 123)(92 124)(93 125)(94 126)(95 127)(96 128)
(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 57 41 85)(2 60 42 88)(3 59 43 87)(4 58 44 86)(5 114 38 24)(6 113 39 23)(7 116 40 22)(8 115 37 21)(9 119 103 25)(10 118 104 28)(11 117 101 27)(12 120 102 26)(13 123 107 29)(14 122 108 32)(15 121 105 31)(16 124 106 30)(17 127 111 33)(18 126 112 36)(19 125 109 35)(20 128 110 34)(45 89 73 61)(46 92 74 64)(47 91 75 63)(48 90 76 62)(49 93 77 66)(50 96 78 65)(51 95 79 68)(52 94 80 67)(53 97 81 70)(54 100 82 69)(55 99 83 72)(56 98 84 71)
(1 109 101 77)(2 52 102 18)(3 111 103 79)(4 50 104 20)(5 32 100 62)(6 89 97 121)(7 30 98 64)(8 91 99 123)(9 51 43 17)(10 110 44 78)(11 49 41 19)(12 112 42 80)(13 55 47 21)(14 114 48 82)(15 53 45 23)(16 116 46 84)(22 74 56 106)(24 76 54 108)(25 33 59 68)(26 94 60 126)(27 35 57 66)(28 96 58 128)(29 37 63 72)(31 39 61 70)(34 118 65 86)(36 120 67 88)(38 122 69 90)(40 124 71 92)(73 113 105 81)(75 115 107 83)(85 93 117 125)(87 95 119 127)
(1 13 9 73)(2 16 10 76)(3 15 11 75)(4 14 12 74)(5 126 71 65)(6 125 72 68)(7 128 69 67)(8 127 70 66)(17 81 77 21)(18 84 78 24)(19 83 79 23)(20 82 80 22)(25 89 85 29)(26 92 86 32)(27 91 87 31)(28 90 88 30)(33 97 93 37)(34 100 94 40)(35 99 95 39)(36 98 96 38)(41 107 103 45)(42 106 104 48)(43 105 101 47)(44 108 102 46)(49 115 111 53)(50 114 112 56)(51 113 109 55)(52 116 110 54)(57 123 119 61)(58 122 120 64)(59 121 117 63)(60 124 118 62)

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

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

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

38 conjugacy classes

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

38 irreducible representations

dim111111112244
type++++++++-+-
imageC1C2C2C2C2C2C2C2Q8C4○D42+ 1+42- 1+4
kernelC23.488C24C4×C4⋊C4C23.63C23C23.65C23C23.67C23C23.78C23C23.81C23C23.83C23C4⋊C4C2×C4C22C22
# reps1261211241611

Matrix representation of C23.488C24 in GL6(𝔽5)

100000
010000
004000
000400
000040
000004
,
400000
040000
001000
000100
000040
000004
,
400000
040000
001000
000100
000010
000001
,
400000
110000
004300
001100
000001
000040
,
100000
440000
003000
002200
000040
000001
,
430000
110000
001000
000100
000040
000001
,
300000
030000
001000
004400
000020
000003

G:=sub<GL(6,GF(5))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,4,0,0,0,0,0,0,4],[4,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,4],[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],[4,1,0,0,0,0,0,1,0,0,0,0,0,0,4,1,0,0,0,0,3,1,0,0,0,0,0,0,0,4,0,0,0,0,1,0],[1,4,0,0,0,0,0,4,0,0,0,0,0,0,3,2,0,0,0,0,0,2,0,0,0,0,0,0,4,0,0,0,0,0,0,1],[4,1,0,0,0,0,3,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,1],[3,0,0,0,0,0,0,3,0,0,0,0,0,0,1,4,0,0,0,0,0,4,0,0,0,0,0,0,2,0,0,0,0,0,0,3] >;

C23.488C24 in GAP, Magma, Sage, TeX

C_2^3._{488}C_2^4
% in TeX

G:=Group("C2^3.488C2^4");
// GroupNames label

G:=SmallGroup(128,1320);
// by ID

G=gap.SmallGroup(128,1320);
# by ID

G:=PCGroup([7,-2,2,2,2,-2,2,2,112,253,792,758,723,352,675,136]);
// Polycyclic

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