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G = C23.263C24  order 128 = 27

116th central extension by C23 of C24

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

Aliases: C23.263C24, C22.942+ 1+4, C22.682- 1+4, C4⋊Q8⋊34C4, C42⋊5C4.6C2, C42.196(C2×C4), C22.154(C23×C4), (C2×C42).451C22, (C22×C4).491C23, (C22×Q8).96C22, C2.43(C22.11C24), C2.C42.71C22, C23.63C23.11C2, C23.67C23.31C2, C2.4(C22.57C24), C2.21(C23.32C23), (C2×C4⋊Q8).28C2, C4⋊C4.112(C2×C4), (C2×C4).59(C22×C4), (C2×Q8).114(C2×C4), (C2×C4⋊C4).198C22, SmallGroup(128,1113)

Series: Derived ►Chief ►Lower central ►Upper central ►Jennings

Derived series
C1 — C22 — C23.263C24
Chief series
C1 — C2 — C22 — C23 — C22×C4 — C2×C42 — C2×C4⋊Q8 — C23.263C24
Lower central
C1 — C22 — C23.263C24
Upper central
C1 — C23 — C23.263C24
Jennings
C1 — C23 — C23.263C24

Generators and relations for C23.263C24
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=c, e2=g2=a, f2=ba=ab, ac=ca, ede-1=ad=da, geg-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, gdg-1=abd, fef-1=abe, fg=gf >

Subgroups: 348 in 212 conjugacy classes, 132 normal (8 characteristic)
C1, C2, C2, C4, C22, C22, C2×C4, C2×C4, Q8, C23, C42, C42, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×Q8, C2×Q8, C2.C42, C2×C42, C2×C42, C2×C4⋊C4, C4⋊Q8, C22×Q8, C42⋊5C4, C23.63C23, C23.67C23, C2×C4⋊Q8, C23.263C24
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, C24, C23×C4, 2+ 1+4, 2- 1+4, C22.11C24, C23.32C23, C22.57C24, C23.263C24

Smallest permutation representation of C23.263C24
►Regular action on 128 points
Generators in S128
(1 11)(2 12)(3 9)(4 10)(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 68)(6 65)(7 66)(8 67)(9 37)(10 38)(11 39)(12 40)(13 41)(14 42)(15 43)(16 44)(17 45)(18 46)(19 47)(20 48)(21 49)(22 50)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(29 57)(30 58)(31 59)(32 60)(33 61)(34 62)(35 63)(36 64)(69 125)(70 126)(71 127)(72 128)(73 101)(74 102)(75 103)(76 104)(77 105)(78 106)(79 107)(80 108)(81 109)(82 110)(83 111)(84 112)(85 113)(86 114)(87 115)(88 116)(89 117)(90 118)(91 119)(92 120)(93 121)(94 122)(95 123)(96 124)

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

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

38 conjugacy classes

class 1 2A···2G4A···4AD
order12···24···4
size11···14···4

38 irreducible representations

dim11111144
type++++++-
imageC1C2C2C2C2C42+ 1+42- 1+4
kernelC23.263C24C42⋊5C4C23.63C23C23.67C23C2×C4⋊Q8C4⋊Q8C22C22
# reps128411624

Matrix representation of C23.263C24 ►in GL9(𝔽5)

100000000
040000000
004000000
000400000
000040000
000004000
000000400
000000040
000000004
,
100000000
010000000
001000000
000100000
000010000
000004000
000000400
000000040
000000004
,
400000000
010000000
001000000
000100000
000010000
000001000
000000100
000000010
000000001
,
300000000
044220000
041300000
003340000
022220000
000000300
000002000
000001021
000003223
,
100000000
002330000
000200000
002000000
033200000
000000010
000003013
000004000
000002340
,
400000000
010300000
000110000
010400000
044100000
000000100
000001000
000003013
000004404
,
100000000
043000000
011000000
004010000
011400000
000003000
000000300
000000020
000004002

G:=sub<GL(9,GF(5))| [1,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,4],[4,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1],[3,0,0,0,0,0,0,0,0,0,4,4,0,2,0,0,0,0,0,4,1,3,2,0,0,0,0,0,2,3,3,2,0,0,0,0,0,2,0,4,2,0,0,0,0,0,0,0,0,0,0,2,1,3,0,0,0,0,0,3,0,0,2,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,1,3],[1,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,2,0,2,3,0,0,0,0,0,3,2,0,2,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,3,4,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,1,1,0,4,0,0,0,0,0,0,3,0,0],[4,0,0,0,0,0,0,0,0,0,1,0,1,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,3,1,4,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,3,4,0,0,0,0,0,1,0,0,4,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,3,4],[1,0,0,0,0,0,0,0,0,0,4,1,0,1,0,0,0,0,0,3,1,4,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,3,0,0,4,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,2] >;
 

C23.263C24 in GAP, Magma, Sage, TeX 

C_2^3._{263}C_2^4
 
% in TeX
 
G:=Group("C2^3.263C2^4");
 
// GroupNames label
 
G:=SmallGroup(128,1113);
 
// by ID
 
G=gap.SmallGroup(128,1113);
 
# by ID
 
G:=PCGroup([7,-2,2,2,2,-2,2,2,448,253,120,758,555,268,1571,346,80]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=1,d^2=c,e^2=g^2=a,f^2=b*a=a*b,a*c=c*a,e*d*e^-1=a*d=d*a,g*e*g^-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,g*d*g^-1=a*b*d,f*e*f^-1=a*b*e,f*g=g*f>;
 
// generators/relations
 

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