p-group, metabelian, nilpotent (class 3), monomial
Aliases: C42.665C23, (C2×C8).34D4, C8⋊C8.5C2, C4.8(C4○D8), C8⋊3Q8.8C2, C8⋊2Q8.9C2, C4⋊Q8.89C22, (C4×C8).258C22, C2.8(C8.2D4), C4.3(C8.C22), C4.SD16.6C2, C2.13(C8.12D4), C22.66(C4⋊1D4), (C2×C4).722(C2×D4), SmallGroup(128,450)
Series: Derived ►Chief ►Lower central ►Upper central ►Jennings
Generators and relations for C42.665C23
G = < a,b,c,d,e | a4=b4=1, c2=a2, d2=ab2, e2=b, ab=ba, cac-1=a-1, ad=da, ae=ea, cbc-1=b-1, bd=db, be=eb, dcd-1=a-1c, ece-1=b-1c, ede-1=a2d >
Subgroups: 176 in 82 conjugacy classes, 36 normal (24 characteristic)
C1, C2, C4, C4, C22, C8, C2×C4, C2×C4, Q8, C42, C4⋊C4, C2×C8, C2×Q8, C4×C8, Q8⋊C4, C4.Q8, C2.D8, C4⋊Q8, C8⋊C8, C4.SD16, C8⋊3Q8, C8⋊2Q8, C42.665C23
Quotients: C1, C2, C22, D4, C23, C2×D4, C4⋊1D4, C4○D8, C8.C22, C8.12D4, C8.2D4, C42.665C23
Character table of C42.665C23
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 8I | 8J | 8K | 8L | |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 16 | 16 | 16 | 16 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | linear of order 2 |
| ρ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | linear of order 2 |
| ρ4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | linear of order 2 |
| ρ7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | -1 | linear of order 2 |
| ρ8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | -1 | 1 | -1 | -1 | linear of order 2 |
| ρ9 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | -2 | 2 | orthogonal lifted from D4 |
| ρ10 | 2 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | 2 | -2 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ11 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | 0 | orthogonal lifted from D4 |
| ρ12 | 2 | 2 | 2 | 2 | -2 | -2 | -2 | 2 | -2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | -2 | 0 | 0 | -2 | 0 | 0 | orthogonal lifted from D4 |
| ρ13 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | -2 | 2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | 2 | -2 | orthogonal lifted from D4 |
| ρ14 | 2 | 2 | 2 | 2 | 2 | -2 | 2 | -2 | -2 | -2 | 0 | 0 | 0 | 0 | -2 | 2 | 0 | 0 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | orthogonal lifted from D4 |
| ρ15 | 2 | -2 | 2 | -2 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | √2 | √2 | √-2 | -√-2 | 0 | -√2 | -√-2 | 2i | -√2 | √-2 | -2i | 0 | complex lifted from C4○D8 |
| ρ16 | 2 | -2 | 2 | -2 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | -√2 | -√2 | -√-2 | √-2 | 0 | √2 | √-2 | 2i | √2 | -√-2 | -2i | 0 | complex lifted from C4○D8 |
| ρ17 | 2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | -√2 | √2 | √-2 | -√-2 | 2i | -√2 | √-2 | 0 | √2 | -√-2 | 0 | -2i | complex lifted from C4○D8 |
| ρ18 | 2 | -2 | 2 | -2 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | -√2 | -√2 | √-2 | -√-2 | 0 | √2 | -√-2 | -2i | √2 | √-2 | 2i | 0 | complex lifted from C4○D8 |
| ρ19 | 2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | √2 | -√2 | √-2 | -√-2 | -2i | √2 | √-2 | 0 | -√2 | -√-2 | 0 | 2i | complex lifted from C4○D8 |
| ρ20 | 2 | -2 | 2 | -2 | 0 | -2 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | √2 | √2 | -√-2 | √-2 | 0 | -√2 | √-2 | -2i | -√2 | -√-2 | 2i | 0 | complex lifted from C4○D8 |
| ρ21 | 2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | √2 | -√2 | -√-2 | √-2 | 2i | √2 | -√-2 | 0 | -√2 | √-2 | 0 | -2i | complex lifted from C4○D8 |
| ρ22 | 2 | -2 | 2 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | 0 | 0 | 0 | 0 | -√2 | √2 | -√-2 | √-2 | -2i | -√2 | -√-2 | 0 | √2 | √-2 | 0 | 2i | complex lifted from C4○D8 |
| ρ23 | 4 | -4 | -4 | 4 | 4 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ24 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ25 | 4 | -4 | -4 | 4 | -4 | 0 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
| ρ26 | 4 | 4 | -4 | -4 | 0 | 0 | 0 | 4 | 0 | -4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | symplectic lifted from C8.C22, Schur index 2 |
►Regular action on 128 points
Generators in S128
(1 23 5 19)(2 24 6 20)(3 17 7 21)(4 18 8 22)(9 41 13 45)(10 42 14 46)(11 43 15 47)(12 44 16 48)(25 53 29 49)(26 54 30 50)(27 55 31 51)(28 56 32 52)(33 122 37 126)(34 123 38 127)(35 124 39 128)(36 125 40 121)(57 76 61 80)(58 77 62 73)(59 78 63 74)(60 79 64 75)(65 102 69 98)(66 103 70 99)(67 104 71 100)(68 97 72 101)(81 106 85 110)(82 107 86 111)(83 108 87 112)(84 109 88 105)(89 114 93 118)(90 115 94 119)(91 116 95 120)(92 117 96 113)
(1 61 21 78)(2 62 22 79)(3 63 23 80)(4 64 24 73)(5 57 17 74)(6 58 18 75)(7 59 19 76)(8 60 20 77)(9 95 47 118)(10 96 48 119)(11 89 41 120)(12 90 42 113)(13 91 43 114)(14 92 44 115)(15 93 45 116)(16 94 46 117)(25 65 51 100)(26 66 52 101)(27 67 53 102)(28 68 54 103)(29 69 55 104)(30 70 56 97)(31 71 49 98)(32 72 50 99)(33 86 128 109)(34 87 121 110)(35 88 122 111)(36 81 123 112)(37 82 124 105)(38 83 125 106)(39 84 126 107)(40 85 127 108)
(1 81 5 85)(2 107 6 111)(3 87 7 83)(4 105 8 109)(9 65 13 69)(10 103 14 99)(11 71 15 67)(12 101 16 97)(17 108 21 112)(18 88 22 84)(19 106 23 110)(20 86 24 82)(25 91 29 95)(26 117 30 113)(27 89 31 93)(28 115 32 119)(33 73 37 77)(34 59 38 63)(35 79 39 75)(36 57 40 61)(41 98 45 102)(42 66 46 70)(43 104 47 100)(44 72 48 68)(49 116 53 120)(50 96 54 92)(51 114 55 118)(52 94 56 90)(58 122 62 126)(60 128 64 124)(74 127 78 123)(76 125 80 121)
(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 98 61 31 21 71 78 49)(2 103 62 28 22 68 79 54)(3 100 63 25 23 65 80 51)(4 97 64 30 24 70 73 56)(5 102 57 27 17 67 74 53)(6 99 58 32 18 72 75 50)(7 104 59 29 19 69 76 55)(8 101 60 26 20 66 77 52)(9 83 95 125 47 106 118 38)(10 88 96 122 48 111 119 35)(11 85 89 127 41 108 120 40)(12 82 90 124 42 105 113 37)(13 87 91 121 43 110 114 34)(14 84 92 126 44 107 115 39)(15 81 93 123 45 112 116 36)(16 86 94 128 46 109 117 33)
G:=sub<Sym(128)| (1,23,5,19)(2,24,6,20)(3,17,7,21)(4,18,8,22)(9,41,13,45)(10,42,14,46)(11,43,15,47)(12,44,16,48)(25,53,29,49)(26,54,30,50)(27,55,31,51)(28,56,32,52)(33,122,37,126)(34,123,38,127)(35,124,39,128)(36,125,40,121)(57,76,61,80)(58,77,62,73)(59,78,63,74)(60,79,64,75)(65,102,69,98)(66,103,70,99)(67,104,71,100)(68,97,72,101)(81,106,85,110)(82,107,86,111)(83,108,87,112)(84,109,88,105)(89,114,93,118)(90,115,94,119)(91,116,95,120)(92,117,96,113), (1,61,21,78)(2,62,22,79)(3,63,23,80)(4,64,24,73)(5,57,17,74)(6,58,18,75)(7,59,19,76)(8,60,20,77)(9,95,47,118)(10,96,48,119)(11,89,41,120)(12,90,42,113)(13,91,43,114)(14,92,44,115)(15,93,45,116)(16,94,46,117)(25,65,51,100)(26,66,52,101)(27,67,53,102)(28,68,54,103)(29,69,55,104)(30,70,56,97)(31,71,49,98)(32,72,50,99)(33,86,128,109)(34,87,121,110)(35,88,122,111)(36,81,123,112)(37,82,124,105)(38,83,125,106)(39,84,126,107)(40,85,127,108), (1,81,5,85)(2,107,6,111)(3,87,7,83)(4,105,8,109)(9,65,13,69)(10,103,14,99)(11,71,15,67)(12,101,16,97)(17,108,21,112)(18,88,22,84)(19,106,23,110)(20,86,24,82)(25,91,29,95)(26,117,30,113)(27,89,31,93)(28,115,32,119)(33,73,37,77)(34,59,38,63)(35,79,39,75)(36,57,40,61)(41,98,45,102)(42,66,46,70)(43,104,47,100)(44,72,48,68)(49,116,53,120)(50,96,54,92)(51,114,55,118)(52,94,56,90)(58,122,62,126)(60,128,64,124)(74,127,78,123)(76,125,80,121), (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), (1,98,61,31,21,71,78,49)(2,103,62,28,22,68,79,54)(3,100,63,25,23,65,80,51)(4,97,64,30,24,70,73,56)(5,102,57,27,17,67,74,53)(6,99,58,32,18,72,75,50)(7,104,59,29,19,69,76,55)(8,101,60,26,20,66,77,52)(9,83,95,125,47,106,118,38)(10,88,96,122,48,111,119,35)(11,85,89,127,41,108,120,40)(12,82,90,124,42,105,113,37)(13,87,91,121,43,110,114,34)(14,84,92,126,44,107,115,39)(15,81,93,123,45,112,116,36)(16,86,94,128,46,109,117,33)>;
G:=Group( (1,23,5,19)(2,24,6,20)(3,17,7,21)(4,18,8,22)(9,41,13,45)(10,42,14,46)(11,43,15,47)(12,44,16,48)(25,53,29,49)(26,54,30,50)(27,55,31,51)(28,56,32,52)(33,122,37,126)(34,123,38,127)(35,124,39,128)(36,125,40,121)(57,76,61,80)(58,77,62,73)(59,78,63,74)(60,79,64,75)(65,102,69,98)(66,103,70,99)(67,104,71,100)(68,97,72,101)(81,106,85,110)(82,107,86,111)(83,108,87,112)(84,109,88,105)(89,114,93,118)(90,115,94,119)(91,116,95,120)(92,117,96,113), (1,61,21,78)(2,62,22,79)(3,63,23,80)(4,64,24,73)(5,57,17,74)(6,58,18,75)(7,59,19,76)(8,60,20,77)(9,95,47,118)(10,96,48,119)(11,89,41,120)(12,90,42,113)(13,91,43,114)(14,92,44,115)(15,93,45,116)(16,94,46,117)(25,65,51,100)(26,66,52,101)(27,67,53,102)(28,68,54,103)(29,69,55,104)(30,70,56,97)(31,71,49,98)(32,72,50,99)(33,86,128,109)(34,87,121,110)(35,88,122,111)(36,81,123,112)(37,82,124,105)(38,83,125,106)(39,84,126,107)(40,85,127,108), (1,81,5,85)(2,107,6,111)(3,87,7,83)(4,105,8,109)(9,65,13,69)(10,103,14,99)(11,71,15,67)(12,101,16,97)(17,108,21,112)(18,88,22,84)(19,106,23,110)(20,86,24,82)(25,91,29,95)(26,117,30,113)(27,89,31,93)(28,115,32,119)(33,73,37,77)(34,59,38,63)(35,79,39,75)(36,57,40,61)(41,98,45,102)(42,66,46,70)(43,104,47,100)(44,72,48,68)(49,116,53,120)(50,96,54,92)(51,114,55,118)(52,94,56,90)(58,122,62,126)(60,128,64,124)(74,127,78,123)(76,125,80,121), (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), (1,98,61,31,21,71,78,49)(2,103,62,28,22,68,79,54)(3,100,63,25,23,65,80,51)(4,97,64,30,24,70,73,56)(5,102,57,27,17,67,74,53)(6,99,58,32,18,72,75,50)(7,104,59,29,19,69,76,55)(8,101,60,26,20,66,77,52)(9,83,95,125,47,106,118,38)(10,88,96,122,48,111,119,35)(11,85,89,127,41,108,120,40)(12,82,90,124,42,105,113,37)(13,87,91,121,43,110,114,34)(14,84,92,126,44,107,115,39)(15,81,93,123,45,112,116,36)(16,86,94,128,46,109,117,33) );
G=PermutationGroup([[(1,23,5,19),(2,24,6,20),(3,17,7,21),(4,18,8,22),(9,41,13,45),(10,42,14,46),(11,43,15,47),(12,44,16,48),(25,53,29,49),(26,54,30,50),(27,55,31,51),(28,56,32,52),(33,122,37,126),(34,123,38,127),(35,124,39,128),(36,125,40,121),(57,76,61,80),(58,77,62,73),(59,78,63,74),(60,79,64,75),(65,102,69,98),(66,103,70,99),(67,104,71,100),(68,97,72,101),(81,106,85,110),(82,107,86,111),(83,108,87,112),(84,109,88,105),(89,114,93,118),(90,115,94,119),(91,116,95,120),(92,117,96,113)], [(1,61,21,78),(2,62,22,79),(3,63,23,80),(4,64,24,73),(5,57,17,74),(6,58,18,75),(7,59,19,76),(8,60,20,77),(9,95,47,118),(10,96,48,119),(11,89,41,120),(12,90,42,113),(13,91,43,114),(14,92,44,115),(15,93,45,116),(16,94,46,117),(25,65,51,100),(26,66,52,101),(27,67,53,102),(28,68,54,103),(29,69,55,104),(30,70,56,97),(31,71,49,98),(32,72,50,99),(33,86,128,109),(34,87,121,110),(35,88,122,111),(36,81,123,112),(37,82,124,105),(38,83,125,106),(39,84,126,107),(40,85,127,108)], [(1,81,5,85),(2,107,6,111),(3,87,7,83),(4,105,8,109),(9,65,13,69),(10,103,14,99),(11,71,15,67),(12,101,16,97),(17,108,21,112),(18,88,22,84),(19,106,23,110),(20,86,24,82),(25,91,29,95),(26,117,30,113),(27,89,31,93),(28,115,32,119),(33,73,37,77),(34,59,38,63),(35,79,39,75),(36,57,40,61),(41,98,45,102),(42,66,46,70),(43,104,47,100),(44,72,48,68),(49,116,53,120),(50,96,54,92),(51,114,55,118),(52,94,56,90),(58,122,62,126),(60,128,64,124),(74,127,78,123),(76,125,80,121)], [(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)], [(1,98,61,31,21,71,78,49),(2,103,62,28,22,68,79,54),(3,100,63,25,23,65,80,51),(4,97,64,30,24,70,73,56),(5,102,57,27,17,67,74,53),(6,99,58,32,18,72,75,50),(7,104,59,29,19,69,76,55),(8,101,60,26,20,66,77,52),(9,83,95,125,47,106,118,38),(10,88,96,122,48,111,119,35),(11,85,89,127,41,108,120,40),(12,82,90,124,42,105,113,37),(13,87,91,121,43,110,114,34),(14,84,92,126,44,107,115,39),(15,81,93,123,45,112,116,36),(16,86,94,128,46,109,117,33)]])
Matrix representation of C42.665C23 ►in GL6(𝔽17)
| 16 | 0 | 0 | 0 | 0 | 0 |
| 0 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 16 | 0 | 0 |
| 0 | 0 | 2 | 16 | 0 | 0 |
| 0 | 0 | 12 | 4 | 4 | 0 |
| 0 | 0 | 7 | 2 | 0 | 13 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 0 | 16 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 0 |
| 0 | 0 | 0 | 0 | 0 | 16 |
| 6 | 4 | 0 | 0 | 0 | 0 |
| 4 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 13 | 13 | 14 | 10 |
| 0 | 0 | 1 | 12 | 2 | 4 |
| 0 | 0 | 14 | 4 | 12 | 11 |
| 0 | 0 | 8 | 1 | 10 | 14 |
| 0 | 13 | 0 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 10 | 15 | 0 | 5 |
| 0 | 0 | 15 | 2 | 2 | 13 |
| 0 | 0 | 1 | 16 | 0 | 0 |
| 5 | 12 | 0 | 0 | 0 | 0 |
| 5 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 5 | 13 | 14 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 2 | 15 | 15 | 4 |
G:=sub<GL(6,GF(17))| [16,0,0,0,0,0,0,16,0,0,0,0,0,0,1,2,12,7,0,0,16,16,4,2,0,0,0,0,4,0,0,0,0,0,0,13],[0,16,0,0,0,0,1,0,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,16],[6,4,0,0,0,0,4,11,0,0,0,0,0,0,13,1,14,8,0,0,13,12,4,1,0,0,14,2,12,10,0,0,10,4,11,14],[0,4,0,0,0,0,13,0,0,0,0,0,0,0,0,10,15,1,0,0,0,15,2,16,0,0,0,0,2,0,0,0,1,5,13,0],[5,5,0,0,0,0,12,5,0,0,0,0,0,0,0,5,16,2,0,0,0,13,0,15,0,0,1,14,0,15,0,0,0,0,0,4] >;
C42.665C23 in GAP, Magma, Sage, TeX
C_4^2._{665}C_2^3 % in TeX
G:=Group("C4^2.665C2^3"); // GroupNames label
G:=SmallGroup(128,450);
// by ID
G=gap.SmallGroup(128,450);
# by ID
G:=PCGroup([7,-2,2,2,-2,2,-2,2,224,141,512,422,387,100,1123,136,2804,172]);
// Polycyclic
G:=Group<a,b,c,d,e|a^4=b^4=1,c^2=a^2,d^2=a*b^2,e^2=b,a*b=b*a,c*a*c^-1=a^-1,a*d=d*a,a*e=e*a,c*b*c^-1=b^-1,b*d=d*b,b*e=e*b,d*c*d^-1=a^-1*c,e*c*e^-1=b^-1*c,e*d*e^-1=a^2*d>;
// generators/relations
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