Copied to
clipboard

## G = C24.636C23order 128 = 27

### 15th central extension by C24 of C23

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

Series: Derived Chief Lower central Upper central Jennings

 Derived series C1 — C23 — C24.636C23
 Chief series C1 — C2 — C22 — C23 — C24 — C23×C4 — Q8×C23 — C24.636C23
 Lower central C1 — C23 — C24.636C23
 Upper central C1 — C24 — C24.636C23
 Jennings C1 — C24 — C24.636C23

Generators and relations for C24.636C23
G = < a,b,c,d,e,f,g | a2=b2=c2=d2=1, e2=d, f2=g2=c, ab=ba, ac=ca, ad=da, fef-1=ae=ea, af=fa, ag=ga, bc=cb, bd=db, geg-1=be=eb, bf=fb, bg=gb, cd=dc, ce=ec, gfg-1=cf=fc, cg=gc, de=ed, df=fd, dg=gd >

Subgroups: 660 in 368 conjugacy classes, 124 normal (6 characteristic)
C1, C2, C2 [×14], C4 [×20], C22 [×35], C2×C4 [×12], C2×C4 [×76], Q8 [×32], C23, C23 [×14], C22×C4 [×26], C22×C4 [×36], C2×Q8 [×56], C24, C2.C42 [×12], C23×C4 [×7], C22×Q8 [×4], C22×Q8 [×12], C2×C2.C42 [×6], Q8×C23, C24.636C23
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C2×C4 [×6], D4 [×12], Q8 [×8], C23, C22⋊C4 [×12], C22×C4, C2×D4 [×6], C2×Q8 [×4], C4○D4 [×4], C2×C22⋊C4 [×3], C4×Q8 [×4], C22≀C2 [×4], C22⋊Q8 [×12], C4.4D4 [×6], C4⋊Q8 [×6], C243C4, C23.67C23 [×6], C23⋊Q8 [×4], C23.78C23 [×4], C24.636C23

Smallest permutation representation of C24.636C23
Regular action on 128 points
Generators in S128
```(1 73)(2 74)(3 75)(4 76)(5 96)(6 93)(7 94)(8 95)(9 13)(10 14)(11 15)(12 16)(17 21)(18 22)(19 23)(20 24)(25 29)(26 30)(27 31)(28 32)(33 71)(34 72)(35 69)(36 70)(37 41)(38 42)(39 43)(40 44)(45 49)(46 50)(47 51)(48 52)(53 57)(54 58)(55 59)(56 60)(61 67)(62 68)(63 65)(64 66)(77 81)(78 82)(79 83)(80 84)(85 89)(86 90)(87 91)(88 92)(97 101)(98 102)(99 103)(100 104)(105 109)(106 110)(107 111)(108 112)(113 117)(114 118)(115 119)(116 120)(121 125)(122 126)(123 127)(124 128)
(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)
(1 115 99 85)(2 120 100 90)(3 113 97 87)(4 118 98 92)(5 80 126 106)(6 81 127 111)(7 78 128 108)(8 83 125 109)(9 55 39 25)(10 60 40 30)(11 53 37 27)(12 58 38 32)(13 59 43 29)(14 56 44 26)(15 57 41 31)(16 54 42 28)(17 63 47 33)(18 66 48 72)(19 61 45 35)(20 68 46 70)(21 65 51 71)(22 64 52 34)(23 67 49 69)(24 62 50 36)(73 119 103 89)(74 116 104 86)(75 117 101 91)(76 114 102 88)(77 123 107 93)(79 121 105 95)(82 124 112 94)(84 122 110 96)
(1 107 99 77)(2 48 100 18)(3 105 97 79)(4 46 98 20)(5 58 126 32)(6 119 127 89)(7 60 128 30)(8 117 125 91)(9 47 39 17)(10 108 40 78)(11 45 37 19)(12 106 38 80)(13 51 43 21)(14 112 44 82)(15 49 41 23)(16 110 42 84)(22 74 52 104)(24 76 50 102)(25 33 55 63)(26 94 56 124)(27 35 53 61)(28 96 54 122)(29 71 59 65)(31 69 57 67)(34 116 64 86)(36 114 62 88)(66 90 72 120)(68 92 70 118)(73 111 103 81)(75 109 101 83)(85 93 115 123)(87 95 113 121)```

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

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

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

44 conjugacy classes

 class 1 2A ··· 2O 4A ··· 4AB order 1 2 ··· 2 4 ··· 4 size 1 1 ··· 1 4 ··· 4

44 irreducible representations

 dim 1 1 1 1 2 2 2 type + + + + - image C1 C2 C2 C4 D4 Q8 C4○D4 kernel C24.636C23 C2×C2.C42 Q8×C23 C22×Q8 C22×C4 C22×C4 C23 # reps 1 6 1 8 12 8 8

Matrix representation of C24.636C23 in GL8(𝔽5)

 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 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 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 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 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 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 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 2 1 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 3 2 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 2 0
,
 4 4 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 1 4 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
,
 4 0 0 0 0 0 0 0 0 4 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 3 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0

`G:=sub<GL(8,GF(5))| [4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[4,2,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,3,1,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,3,0],[4,0,0,0,0,0,0,0,4,1,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0],[4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,2,2,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0] >;`

C24.636C23 in GAP, Magma, Sage, TeX

`C_2^4._{636}C_2^3`
`% in TeX`

`G:=Group("C2^4.636C2^3");`
`// GroupNames label`

`G:=SmallGroup(128,178);`
`// by ID`

`G=gap.SmallGroup(128,178);`
`# by ID`

`G:=PCGroup([7,-2,2,2,-2,2,2,2,448,141,232,422,387,184]);`
`// Polycyclic`

`G:=Group<a,b,c,d,e,f,g|a^2=b^2=c^2=d^2=1,e^2=d,f^2=g^2=c,a*b=b*a,a*c=c*a,a*d=d*a,f*e*f^-1=a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,b*d=d*b,g*e*g^-1=b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,c*e=e*c,g*f*g^-1=c*f=f*c,c*g=g*c,d*e=e*d,d*f=f*d,d*g=g*d>;`
`// generators/relations`

׿
×
𝔽