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G = C23.218C24order 128 = 27

71st central extension by C23 of C24

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

Aliases: C23.218C24, C22.392- 1+4, C22.562+ 1+4, C42.C214C4, C425C4.4C2, C42.183(C2×C4), (C2×C42).422C22, (C22×C4).483C23, C22.109(C23×C4), C2.C42.53C22, C23.63C23.5C2, C23.65C23.32C2, C2.9(C22.33C24), C2.7(C22.35C24), C2.20(C23.33C23), C2.12(C23.32C23), (C4×C4⋊C4).37C2, C2.21(C4×C4○D4), C4⋊C4.107(C2×C4), (C2×C4).38(C22×C4), (C2×C4).520(C4○D4), (C2×C4⋊C4).813C22, C22.103(C2×C4○D4), (C2×C42.C2).12C2, SmallGroup(128,1068)

Series: Derived Chief Lower central Upper central Jennings

C1C22 — C23.218C24
C1C2C22C23C22×C4C2×C42C4×C4⋊C4 — C23.218C24
C1C22 — C23.218C24
C1C23 — C23.218C24
C1C23 — C23.218C24

Generators and relations for C23.218C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=e2=c, f2=a, g2=ba=ab, ac=ca, ede-1=gdg-1=ad=da, fef-1=ae=ea, af=fa, ag=ga, bc=cb, fdf-1=bd=db, be=eb, bf=fb, bg=gb, cd=dc, ce=ec, cf=fc, cg=gc, eg=ge, fg=gf >

Subgroups: 316 in 214 conjugacy classes, 136 normal (22 characteristic)
C1, C2 [×3], C2 [×4], C4 [×24], C22 [×3], C22 [×4], C2×C4 [×18], C2×C4 [×36], C23, C42 [×4], C42 [×8], C4⋊C4 [×24], C4⋊C4 [×10], C22×C4 [×3], C22×C4 [×12], C2.C42 [×2], C2.C42 [×14], C2×C42 [×3], C2×C42 [×4], C2×C4⋊C4 [×2], C2×C4⋊C4 [×10], C42.C2 [×8], C4×C4⋊C4, C4×C4⋊C4 [×2], C425C4, C23.63C23 [×8], C23.65C23 [×2], C2×C42.C2, C23.218C24
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], C22×C4 [×14], C4○D4 [×4], C24, C23×C4, C2×C4○D4 [×2], 2+ 1+4, 2- 1+4 [×3], C4×C4○D4, C23.32C23, C23.33C23, C22.33C24 [×2], C22.35C24 [×2], C23.218C24

Smallest permutation representation of C23.218C24
Regular action on 128 points
Generators in S128
(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 87 3 85)(2 28 4 26)(5 24 7 22)(6 81 8 83)(9 27 11 25)(10 88 12 86)(13 31 15 29)(14 92 16 90)(17 35 19 33)(18 96 20 94)(21 69 23 71)(30 74 32 76)(34 78 36 80)(37 55 39 53)(38 116 40 114)(41 59 43 57)(42 120 44 118)(45 63 47 61)(46 124 48 122)(49 65 51 67)(50 128 52 126)(54 98 56 100)(58 102 60 104)(62 106 64 108)(66 112 68 110)(70 84 72 82)(73 91 75 89)(77 95 79 93)(97 115 99 113)(101 119 103 117)(105 123 107 121)(109 127 111 125)
(1 17 9 77)(2 48 10 108)(3 19 11 79)(4 46 12 106)(5 58 70 118)(6 29 71 89)(7 60 72 120)(8 31 69 91)(13 81 73 21)(14 112 74 52)(15 83 75 23)(16 110 76 50)(18 40 78 100)(20 38 80 98)(22 44 82 104)(24 42 84 102)(25 33 85 93)(26 64 86 124)(27 35 87 95)(28 62 88 122)(30 66 90 128)(32 68 92 126)(34 116 94 56)(36 114 96 54)(37 105 97 45)(39 107 99 47)(41 109 101 49)(43 111 103 51)(53 61 113 121)(55 63 115 123)(57 67 117 125)(59 65 119 127)
(1 43 39 73)(2 104 40 14)(3 41 37 75)(4 102 38 16)(5 36 68 122)(6 93 65 63)(7 34 66 124)(8 95 67 61)(9 103 99 13)(10 44 100 74)(11 101 97 15)(12 42 98 76)(17 111 107 21)(18 52 108 82)(19 109 105 23)(20 50 106 84)(22 78 112 48)(24 80 110 46)(25 119 115 29)(26 60 116 90)(27 117 113 31)(28 58 114 92)(30 86 120 56)(32 88 118 54)(33 127 123 71)(35 125 121 69)(45 83 79 49)(47 81 77 51)(53 91 87 57)(55 89 85 59)(62 70 96 126)(64 72 94 128)

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

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

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

44 conjugacy classes

class 1 2A···2G4A···4L4M···4AJ
order12···24···44···4
size11···12···24···4

44 irreducible representations

dim1111111244
type+++++++-
imageC1C2C2C2C2C2C4C4○D42+ 1+42- 1+4
kernelC23.218C24C4×C4⋊C4C425C4C23.63C23C23.65C23C2×C42.C2C42.C2C2×C4C22C22
# reps13182116813

Matrix representation of C23.218C24 in GL8(𝔽5)

10000000
01000000
00100000
00010000
00004000
00000400
00000040
00000004
,
40000000
04000000
00400000
00040000
00001000
00000100
00000010
00000001
,
40000000
04000000
00100000
00010000
00004000
00000400
00000040
00000004
,
20000000
03000000
00330000
00420000
00000010
00000001
00004000
00000400
,
30000000
03000000
00100000
00010000
00002000
00000300
00000030
00000002
,
01000000
10000000
00110000
00040000
00000100
00004000
00000001
00000040
,
30000000
03000000
00300000
00030000
00002000
00000200
00000030
00000003

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],[4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4],[2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,3,4,0,0,0,0,0,0,3,2,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0],[3,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,2],[0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0],[3,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,3] >;

C23.218C24 in GAP, Magma, Sage, TeX

C_2^3._{218}C_2^4
% in TeX

G:=Group("C2^3.218C2^4");
// GroupNames label

G:=SmallGroup(128,1068);
// by ID

G=gap.SmallGroup(128,1068);
# by ID

G:=PCGroup([7,-2,2,2,2,-2,2,2,448,253,456,758,219,100,675,192]);
// Polycyclic

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