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G = C23.253C24  order 128 = 27

106th central extension by C23 of C24

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

Aliases: C23.253C24, C22.622- (1+4), C42.C2⋊16C4, C42.195(C2×C4), C42⋊4C4.17C2, (C2×C42).443C22, (C22×C4).772C23, C22.144(C23×C4), C23.63C23.10C2, C2.C42.480C22, C2.10(C22.46C24), C2.19(C23.32C23), (C4×C4⋊C4).45C2, C2.40(C4×C4○D4), C4⋊C4.110(C2×C4), (C2×C4).51(C22×C4), (C2×C4).725(C4○D4), (C2×C4⋊C4).830C22, C22.138(C2×C4○D4), (C2×C42.C2).14C2, SmallGroup(128,1103)

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

Derived series
C1 — C22 — C23.253C24
Chief series
C1 — C2 — C22 — C23 — C22×C4 — C2×C42 — C42⋊4C4 — C23.253C24
Lower central
C1 — C22 — C23.253C24
Upper central
C1 — C23 — C23.253C24
Jennings
C1 — C23 — C23.253C24

Subgroups: 316 in 224 conjugacy classes, 140 normal (8 characteristic)
C1, C2, C2 [×6], C4 [×26], C22, C22 [×6], C2×C4 [×22], C2×C4 [×34], C23, C42 [×4], C42 [×16], C4⋊C4 [×24], C4⋊C4 [×8], C22×C4, C22×C4 [×14], C2.C42 [×16], C2×C42, C2×C42 [×8], C2×C4⋊C4 [×10], C42.C2 [×8], C42⋊4C4 [×2], C4×C4⋊C4 [×4], C23.63C23 [×8], C2×C42.C2, C23.253C24

Quotients:
C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], C23 [×15], C22×C4 [×14], C4○D4 [×8], C24, C23×C4, C2×C4○D4 [×4], 2- (1+4) [×2], C4×C4○D4 [×2], C23.32C23, C22.46C24 [×4], C23.253C24

Generators and relations
 G = < a,b,c,d,e,f,g | a2=b2=c2=1, d2=e2=c, f2=a, g2=b, ab=ba, 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, dg=gd, ef=fe, fg=gf >

Smallest permutation representation
►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)(5 118 70 58)(6 89 71 29)(7 120 72 60)(8 91 69 31)(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 93 85 33)(26 124 86 64)(27 95 87 35)(28 122 88 62)(30 128 90 66)(32 126 92 68)(34 56 94 116)(36 54 96 114)(37 105 97 45)(39 107 99 47)(41 109 101 49)(43 111 103 51)(53 121 113 61)(55 123 115 63)(57 125 117 67)(59 127 119 65)

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

Matrix representation ►G ⊆ GL5(𝔽5)

10000
01000
00100
00040
00004
,
10000
04000
00400
00010
00001
,
40000
01000
00100
00040
00004
,
30000
00100
01000
00003
00030
,
20000
04000
00400
00004
00010
,
10000
04000
00100
00030
00003
,
40000
02000
00200
00001
00010

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

50 conjugacy classes

class 1 2A···2G4A···4X4Y···4AP
order12···24···44···4
size11···12···24···4

50 irreducible representations

dim11111124
type+++++-
imageC1C2C2C2C2C4C4○D42- (1+4)
kernelC23.253C24C42⋊4C4C4×C4⋊C4C23.63C23C2×C42.C2C42.C2C2×C4C22
# reps1248116162

In GAP, Magma, Sage, TeX 

C_2^3._{253}C_2^4
 
% in TeX
 
G:=Group("C2^3.253C2^4");
 
// GroupNames label
 
G:=SmallGroup(128,1103);
 
// by ID
 
G=gap.SmallGroup(128,1103);
 
# by ID
 
G:=PCGroup([7,-2,2,2,2,-2,2,2,448,253,456,758,100,346,136]);
 
// 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*b=b*a,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,d*g=g*d,e*f=f*e,f*g=g*f>;
 
// generators/relations
 

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