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G = C23.202C24order 128 = 27

55th central extension by C23 of C24

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

Aliases: C23.202C24, C22.412+ 1+4, C22.262- 1+4, (C4×Q8)⋊18C4, C425C4.3C2, C42.179(C2×C4), C428C4.19C2, C424C4.12C2, C22.93(C23×C4), C4.15(C42⋊C2), (C22×C4).467C23, (C2×C42).410C22, (C22×Q8).397C22, C2.C42.39C22, C23.63C23.1C2, C23.67C23.24C2, C23.65C23.29C2, C2.3(C22.36C24), C2.2(C22.35C24), C2.7(C23.32C23), C2.10(C23.33C23), (C4×C4⋊C4).34C2, (C2×C4×Q8).21C2, C4⋊C4.205(C2×C4), (C2×Q8).193(C2×C4), C22.87(C2×C4○D4), (C2×C4).645(C4○D4), (C2×C4⋊C4).176C22, (C2×C4).225(C22×C4), C2.24(C2×C42⋊C2), SmallGroup(128,1052)

Series: Derived Chief Lower central Upper central Jennings

C1C22 — C23.202C24
C1C2C22C23C22×C4C2×C42C2×C4×Q8 — C23.202C24
C1C22 — C23.202C24
C1C23 — C23.202C24
C1C23 — C23.202C24

Generators and relations for C23.202C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=c, e2=f2=a, g2=b, ab=ba, 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: 332 in 222 conjugacy classes, 140 normal (20 characteristic)
C1, C2 [×3], C2 [×4], C4 [×4], C4 [×20], C22 [×3], C22 [×4], C2×C4 [×18], C2×C4 [×36], Q8 [×8], C23, C42 [×12], C42 [×6], C4⋊C4 [×12], C4⋊C4 [×8], C22×C4 [×3], C22×C4 [×12], C2×Q8 [×4], C2×Q8 [×4], C2.C42 [×2], C2.C42 [×16], C2×C42, C2×C42 [×6], C2×C4⋊C4, C2×C4⋊C4 [×8], C4×Q8 [×8], C22×Q8, C424C4, C4×C4⋊C4, C428C4 [×2], C425C4 [×2], C23.63C23 [×4], C23.65C23 [×2], C23.67C23 [×2], C2×C4×Q8, C23.202C24
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], C22×C4 [×14], C4○D4 [×4], C24, C42⋊C2 [×4], C23×C4, C2×C4○D4 [×2], 2+ 1+4, 2- 1+4 [×3], C2×C42⋊C2, C23.32C23, C23.33C23, C22.35C24 [×2], C22.36C24 [×2], C23.202C24

Smallest permutation representation of C23.202C24
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 25 9 85)(2 86 10 26)(3 27 11 87)(4 88 12 28)(5 24 70 84)(6 81 71 21)(7 22 72 82)(8 83 69 23)(13 89 73 29)(14 30 74 90)(15 91 75 31)(16 32 76 92)(17 93 77 33)(18 34 78 94)(19 95 79 35)(20 36 80 96)(37 113 97 53)(38 54 98 114)(39 115 99 55)(40 56 100 116)(41 117 101 57)(42 58 102 118)(43 119 103 59)(44 60 104 120)(45 121 105 61)(46 62 106 122)(47 123 107 63)(48 64 108 124)(49 125 109 67)(50 68 110 126)(51 127 111 65)(52 66 112 128)
(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)
(1 103 99 73)(2 44 100 14)(3 101 97 75)(4 42 98 16)(5 36 126 62)(6 93 127 123)(7 34 128 64)(8 95 125 121)(9 43 39 13)(10 104 40 74)(11 41 37 15)(12 102 38 76)(17 51 47 21)(18 112 48 82)(19 49 45 23)(20 110 46 84)(22 78 52 108)(24 80 50 106)(25 59 55 29)(26 120 56 90)(27 57 53 31)(28 118 54 92)(30 86 60 116)(32 88 58 114)(33 65 63 71)(35 67 61 69)(66 124 72 94)(68 122 70 96)(77 111 107 81)(79 109 105 83)(85 119 115 89)(87 117 113 91)

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

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

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

44 conjugacy classes

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

44 irreducible representations

dim1111111111244
type++++++++++-
imageC1C2C2C2C2C2C2C2C2C4C4○D42+ 1+42- 1+4
kernelC23.202C24C424C4C4×C4⋊C4C428C4C425C4C23.63C23C23.65C23C23.67C23C2×C4×Q8C4×Q8C2×C4C22C22
# reps11122422116813

Matrix representation of C23.202C24 in GL8(𝔽5)

10000000
01000000
00100000
00010000
00004000
00000400
00000040
00000004
,
40000000
04000000
00400000
00040000
00001000
00000100
00000010
00000001
,
10000000
01000000
00400000
00040000
00004000
00000400
00000040
00000004
,
10000000
24000000
00320000
00020000
00001434
00004241
00000132
00003034
,
10000000
01000000
00400000
00040000
00000001
00004411
00000312
00004000
,
41000000
01000000
00320000
00120000
00000010
00002240
00004000
00000243
,
30000000
03000000
00200000
00020000
00000100
00001000
00002240
00004411

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

C23.202C24 in GAP, Magma, Sage, TeX

C_2^3._{202}C_2^4
% in TeX

G:=Group("C2^3.202C2^4");
// GroupNames label

G:=SmallGroup(128,1052);
// by ID

G=gap.SmallGroup(128,1052);
# by ID

G:=PCGroup([7,-2,2,2,2,-2,2,2,448,253,120,758,219,100,675,136]);
// Polycyclic

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