metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C30.4D4, C20.3D6, C15⋊1SD16, Dic6⋊2D5, D20.2S3, C12.3D10, C60.23C22, C3⋊2(Q8⋊D5), C15⋊3C8⋊7C2, C5⋊2(D4.S3), C4.16(S3×D5), (C5×Dic6)⋊4C2, (C3×D20).2C2, C6.8(C5⋊D4), C10.8(C3⋊D4), C2.5(C15⋊D4), SmallGroup(240,16)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C30.D4
G = < a,b,c | a20=b6=1, c2=a15, bab-1=a-1, cac-1=a9, cbc-1=a5b-1 >
Character table of C30.D4
| class | 1 | 2A | 2B | 3 | 4A | 4B | 5A | 5B | 6A | 6B | 6C | 8A | 8B | 10A | 10B | 12 | 15A | 15B | 20A | 20B | 20C | 20D | 20E | 20F | 30A | 30B | 60A | 60B | 60C | 60D | |
| size | 1 | 1 | 20 | 2 | 2 | 12 | 2 | 2 | 2 | 20 | 20 | 30 | 30 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 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 | 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 | 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 | 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 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ5 | 2 | 2 | 0 | 2 | -2 | 0 | 2 | 2 | 2 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | 2 | 2 | -2 | -2 | 0 | 0 | 0 | 0 | 2 | 2 | -2 | -2 | -2 | -2 | orthogonal lifted from D4 |
| ρ6 | 2 | 2 | -2 | -1 | 2 | 0 | 2 | 2 | -1 | 1 | 1 | 0 | 0 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from D6 |
| ρ7 | 2 | 2 | 2 | -1 | 2 | 0 | 2 | 2 | -1 | -1 | -1 | 0 | 0 | 2 | 2 | -1 | -1 | -1 | 2 | 2 | 0 | 0 | 0 | 0 | -1 | -1 | -1 | -1 | -1 | -1 | orthogonal lifted from S3 |
| ρ8 | 2 | 2 | 0 | 2 | 2 | 2 | -1+√5/2 | -1-√5/2 | 2 | 0 | 0 | 0 | 0 | -1+√5/2 | -1-√5/2 | 2 | -1+√5/2 | -1-√5/2 | -1+√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | orthogonal lifted from D5 |
| ρ9 | 2 | 2 | 0 | 2 | 2 | 2 | -1-√5/2 | -1+√5/2 | 2 | 0 | 0 | 0 | 0 | -1-√5/2 | -1+√5/2 | 2 | -1-√5/2 | -1+√5/2 | -1-√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | orthogonal lifted from D5 |
| ρ10 | 2 | 2 | 0 | 2 | 2 | -2 | -1+√5/2 | -1-√5/2 | 2 | 0 | 0 | 0 | 0 | -1+√5/2 | -1-√5/2 | 2 | -1+√5/2 | -1-√5/2 | -1+√5/2 | -1-√5/2 | 1-√5/2 | 1-√5/2 | 1+√5/2 | 1+√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | orthogonal lifted from D10 |
| ρ11 | 2 | 2 | 0 | 2 | 2 | -2 | -1-√5/2 | -1+√5/2 | 2 | 0 | 0 | 0 | 0 | -1-√5/2 | -1+√5/2 | 2 | -1-√5/2 | -1+√5/2 | -1-√5/2 | -1+√5/2 | 1+√5/2 | 1+√5/2 | 1-√5/2 | 1-√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | orthogonal lifted from D10 |
| ρ12 | 2 | 2 | 0 | -1 | -2 | 0 | 2 | 2 | -1 | √-3 | -√-3 | 0 | 0 | 2 | 2 | 1 | -1 | -1 | -2 | -2 | 0 | 0 | 0 | 0 | -1 | -1 | 1 | 1 | 1 | 1 | complex lifted from C3⋊D4 |
| ρ13 | 2 | 2 | 0 | -1 | -2 | 0 | 2 | 2 | -1 | -√-3 | √-3 | 0 | 0 | 2 | 2 | 1 | -1 | -1 | -2 | -2 | 0 | 0 | 0 | 0 | -1 | -1 | 1 | 1 | 1 | 1 | complex lifted from C3⋊D4 |
| ρ14 | 2 | 2 | 0 | 2 | -2 | 0 | -1-√5/2 | -1+√5/2 | 2 | 0 | 0 | 0 | 0 | -1-√5/2 | -1+√5/2 | -2 | -1-√5/2 | -1+√5/2 | 1+√5/2 | 1-√5/2 | ζ53-ζ52 | -ζ53+ζ52 | ζ54-ζ5 | -ζ54+ζ5 | -1+√5/2 | -1-√5/2 | 1+√5/2 | 1-√5/2 | 1-√5/2 | 1+√5/2 | complex lifted from C5⋊D4 |
| ρ15 | 2 | 2 | 0 | 2 | -2 | 0 | -1+√5/2 | -1-√5/2 | 2 | 0 | 0 | 0 | 0 | -1+√5/2 | -1-√5/2 | -2 | -1+√5/2 | -1-√5/2 | 1-√5/2 | 1+√5/2 | ζ54-ζ5 | -ζ54+ζ5 | -ζ53+ζ52 | ζ53-ζ52 | -1-√5/2 | -1+√5/2 | 1-√5/2 | 1+√5/2 | 1+√5/2 | 1-√5/2 | complex lifted from C5⋊D4 |
| ρ16 | 2 | 2 | 0 | 2 | -2 | 0 | -1-√5/2 | -1+√5/2 | 2 | 0 | 0 | 0 | 0 | -1-√5/2 | -1+√5/2 | -2 | -1-√5/2 | -1+√5/2 | 1+√5/2 | 1-√5/2 | -ζ53+ζ52 | ζ53-ζ52 | -ζ54+ζ5 | ζ54-ζ5 | -1+√5/2 | -1-√5/2 | 1+√5/2 | 1-√5/2 | 1-√5/2 | 1+√5/2 | complex lifted from C5⋊D4 |
| ρ17 | 2 | 2 | 0 | 2 | -2 | 0 | -1+√5/2 | -1-√5/2 | 2 | 0 | 0 | 0 | 0 | -1+√5/2 | -1-√5/2 | -2 | -1+√5/2 | -1-√5/2 | 1-√5/2 | 1+√5/2 | -ζ54+ζ5 | ζ54-ζ5 | ζ53-ζ52 | -ζ53+ζ52 | -1-√5/2 | -1+√5/2 | 1-√5/2 | 1+√5/2 | 1+√5/2 | 1-√5/2 | complex lifted from C5⋊D4 |
| ρ18 | 2 | -2 | 0 | 2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | √-2 | -√-2 | -2 | -2 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | complex lifted from SD16 |
| ρ19 | 2 | -2 | 0 | 2 | 0 | 0 | 2 | 2 | -2 | 0 | 0 | -√-2 | √-2 | -2 | -2 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | complex lifted from SD16 |
| ρ20 | 4 | 4 | 0 | -2 | 4 | 0 | -1-√5 | -1+√5 | -2 | 0 | 0 | 0 | 0 | -1-√5 | -1+√5 | -2 | 1+√5/2 | 1-√5/2 | -1-√5 | -1+√5 | 0 | 0 | 0 | 0 | 1-√5/2 | 1+√5/2 | 1+√5/2 | 1-√5/2 | 1-√5/2 | 1+√5/2 | orthogonal lifted from S3×D5 |
| ρ21 | 4 | 4 | 0 | -2 | 4 | 0 | -1+√5 | -1-√5 | -2 | 0 | 0 | 0 | 0 | -1+√5 | -1-√5 | -2 | 1-√5/2 | 1+√5/2 | -1+√5 | -1-√5 | 0 | 0 | 0 | 0 | 1+√5/2 | 1-√5/2 | 1-√5/2 | 1+√5/2 | 1+√5/2 | 1-√5/2 | orthogonal lifted from S3×D5 |
| ρ22 | 4 | -4 | 0 | 4 | 0 | 0 | -1-√5 | -1+√5 | -4 | 0 | 0 | 0 | 0 | 1+√5 | 1-√5 | 0 | -1-√5 | -1+√5 | 0 | 0 | 0 | 0 | 0 | 0 | 1-√5 | 1+√5 | 0 | 0 | 0 | 0 | orthogonal lifted from Q8⋊D5, Schur index 2 |
| ρ23 | 4 | -4 | 0 | 4 | 0 | 0 | -1+√5 | -1-√5 | -4 | 0 | 0 | 0 | 0 | 1-√5 | 1+√5 | 0 | -1+√5 | -1-√5 | 0 | 0 | 0 | 0 | 0 | 0 | 1+√5 | 1-√5 | 0 | 0 | 0 | 0 | orthogonal lifted from Q8⋊D5, Schur index 2 |
| ρ24 | 4 | -4 | 0 | -2 | 0 | 0 | 4 | 4 | 2 | 0 | 0 | 0 | 0 | -4 | -4 | 0 | -2 | -2 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 0 | 0 | 0 | symplectic lifted from D4.S3, Schur index 2 |
| ρ25 | 4 | 4 | 0 | -2 | -4 | 0 | -1+√5 | -1-√5 | -2 | 0 | 0 | 0 | 0 | -1+√5 | -1-√5 | 2 | 1-√5/2 | 1+√5/2 | 1-√5 | 1+√5 | 0 | 0 | 0 | 0 | 1+√5/2 | 1-√5/2 | -1+√5/2 | -1-√5/2 | -1-√5/2 | -1+√5/2 | symplectic lifted from C15⋊D4, Schur index 2 |
| ρ26 | 4 | 4 | 0 | -2 | -4 | 0 | -1-√5 | -1+√5 | -2 | 0 | 0 | 0 | 0 | -1-√5 | -1+√5 | 2 | 1+√5/2 | 1-√5/2 | 1+√5 | 1-√5 | 0 | 0 | 0 | 0 | 1-√5/2 | 1+√5/2 | -1-√5/2 | -1+√5/2 | -1+√5/2 | -1-√5/2 | symplectic lifted from C15⋊D4, Schur index 2 |
| ρ27 | 4 | -4 | 0 | -2 | 0 | 0 | -1-√5 | -1+√5 | 2 | 0 | 0 | 0 | 0 | 1+√5 | 1-√5 | 0 | 1+√5/2 | 1-√5/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√5/2 | -1-√5/2 | -2ζ4ζ3ζ53+2ζ4ζ3ζ52-ζ4ζ53+ζ4ζ52 | 2ζ4ζ3ζ54-2ζ4ζ3ζ5+ζ4ζ54-ζ4ζ5 | 2ζ43ζ3ζ54-2ζ43ζ3ζ5+ζ43ζ54-ζ43ζ5 | -2ζ43ζ3ζ53+2ζ43ζ3ζ52-ζ43ζ53+ζ43ζ52 | complex faithful |
| ρ28 | 4 | -4 | 0 | -2 | 0 | 0 | -1-√5 | -1+√5 | 2 | 0 | 0 | 0 | 0 | 1+√5 | 1-√5 | 0 | 1+√5/2 | 1-√5/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1+√5/2 | -1-√5/2 | -2ζ43ζ3ζ53+2ζ43ζ3ζ52-ζ43ζ53+ζ43ζ52 | 2ζ43ζ3ζ54-2ζ43ζ3ζ5+ζ43ζ54-ζ43ζ5 | 2ζ4ζ3ζ54-2ζ4ζ3ζ5+ζ4ζ54-ζ4ζ5 | -2ζ4ζ3ζ53+2ζ4ζ3ζ52-ζ4ζ53+ζ4ζ52 | complex faithful |
| ρ29 | 4 | -4 | 0 | -2 | 0 | 0 | -1+√5 | -1-√5 | 2 | 0 | 0 | 0 | 0 | 1-√5 | 1+√5 | 0 | 1-√5/2 | 1+√5/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√5/2 | -1+√5/2 | 2ζ4ζ3ζ54-2ζ4ζ3ζ5+ζ4ζ54-ζ4ζ5 | -2ζ43ζ3ζ53+2ζ43ζ3ζ52-ζ43ζ53+ζ43ζ52 | -2ζ4ζ3ζ53+2ζ4ζ3ζ52-ζ4ζ53+ζ4ζ52 | 2ζ43ζ3ζ54-2ζ43ζ3ζ5+ζ43ζ54-ζ43ζ5 | complex faithful |
| ρ30 | 4 | -4 | 0 | -2 | 0 | 0 | -1+√5 | -1-√5 | 2 | 0 | 0 | 0 | 0 | 1-√5 | 1+√5 | 0 | 1-√5/2 | 1+√5/2 | 0 | 0 | 0 | 0 | 0 | 0 | -1-√5/2 | -1+√5/2 | 2ζ43ζ3ζ54-2ζ43ζ3ζ5+ζ43ζ54-ζ43ζ5 | -2ζ4ζ3ζ53+2ζ4ζ3ζ52-ζ4ζ53+ζ4ζ52 | -2ζ43ζ3ζ53+2ζ43ζ3ζ52-ζ43ζ53+ζ43ζ52 | 2ζ4ζ3ζ54-2ζ4ζ3ζ5+ζ4ζ54-ζ4ζ5 | complex faithful |
►On 120 points
Generators in S120
(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)
(1 106 33)(2 105 34 20 107 32)(3 104 35 19 108 31)(4 103 36 18 109 30)(5 102 37 17 110 29)(6 101 38 16 111 28)(7 120 39 15 112 27)(8 119 40 14 113 26)(9 118 21 13 114 25)(10 117 22 12 115 24)(11 116 23)(41 96 74 50 87 63)(42 95 75 49 88 62)(43 94 76 48 89 61)(44 93 77 47 90 80)(45 92 78 46 91 79)(51 86 64 60 97 73)(52 85 65 59 98 72)(53 84 66 58 99 71)(54 83 67 57 100 70)(55 82 68 56 81 69)
(1 58 16 53 11 48 6 43)(2 47 17 42 12 57 7 52)(3 56 18 51 13 46 8 41)(4 45 19 60 14 55 9 50)(5 54 20 49 15 44 10 59)(21 96 36 91 31 86 26 81)(22 85 37 100 32 95 27 90)(23 94 38 89 33 84 28 99)(24 83 39 98 34 93 29 88)(25 92 40 87 35 82 30 97)(61 111 76 106 71 101 66 116)(62 120 77 115 72 110 67 105)(63 109 78 104 73 119 68 114)(64 118 79 113 74 108 69 103)(65 107 80 102 75 117 70 112)
G:=sub<Sym(120)| (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), (1,106,33)(2,105,34,20,107,32)(3,104,35,19,108,31)(4,103,36,18,109,30)(5,102,37,17,110,29)(6,101,38,16,111,28)(7,120,39,15,112,27)(8,119,40,14,113,26)(9,118,21,13,114,25)(10,117,22,12,115,24)(11,116,23)(41,96,74,50,87,63)(42,95,75,49,88,62)(43,94,76,48,89,61)(44,93,77,47,90,80)(45,92,78,46,91,79)(51,86,64,60,97,73)(52,85,65,59,98,72)(53,84,66,58,99,71)(54,83,67,57,100,70)(55,82,68,56,81,69), (1,58,16,53,11,48,6,43)(2,47,17,42,12,57,7,52)(3,56,18,51,13,46,8,41)(4,45,19,60,14,55,9,50)(5,54,20,49,15,44,10,59)(21,96,36,91,31,86,26,81)(22,85,37,100,32,95,27,90)(23,94,38,89,33,84,28,99)(24,83,39,98,34,93,29,88)(25,92,40,87,35,82,30,97)(61,111,76,106,71,101,66,116)(62,120,77,115,72,110,67,105)(63,109,78,104,73,119,68,114)(64,118,79,113,74,108,69,103)(65,107,80,102,75,117,70,112)>;
G:=Group( (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), (1,106,33)(2,105,34,20,107,32)(3,104,35,19,108,31)(4,103,36,18,109,30)(5,102,37,17,110,29)(6,101,38,16,111,28)(7,120,39,15,112,27)(8,119,40,14,113,26)(9,118,21,13,114,25)(10,117,22,12,115,24)(11,116,23)(41,96,74,50,87,63)(42,95,75,49,88,62)(43,94,76,48,89,61)(44,93,77,47,90,80)(45,92,78,46,91,79)(51,86,64,60,97,73)(52,85,65,59,98,72)(53,84,66,58,99,71)(54,83,67,57,100,70)(55,82,68,56,81,69), (1,58,16,53,11,48,6,43)(2,47,17,42,12,57,7,52)(3,56,18,51,13,46,8,41)(4,45,19,60,14,55,9,50)(5,54,20,49,15,44,10,59)(21,96,36,91,31,86,26,81)(22,85,37,100,32,95,27,90)(23,94,38,89,33,84,28,99)(24,83,39,98,34,93,29,88)(25,92,40,87,35,82,30,97)(61,111,76,106,71,101,66,116)(62,120,77,115,72,110,67,105)(63,109,78,104,73,119,68,114)(64,118,79,113,74,108,69,103)(65,107,80,102,75,117,70,112) );
G=PermutationGroup([[(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)], [(1,106,33),(2,105,34,20,107,32),(3,104,35,19,108,31),(4,103,36,18,109,30),(5,102,37,17,110,29),(6,101,38,16,111,28),(7,120,39,15,112,27),(8,119,40,14,113,26),(9,118,21,13,114,25),(10,117,22,12,115,24),(11,116,23),(41,96,74,50,87,63),(42,95,75,49,88,62),(43,94,76,48,89,61),(44,93,77,47,90,80),(45,92,78,46,91,79),(51,86,64,60,97,73),(52,85,65,59,98,72),(53,84,66,58,99,71),(54,83,67,57,100,70),(55,82,68,56,81,69)], [(1,58,16,53,11,48,6,43),(2,47,17,42,12,57,7,52),(3,56,18,51,13,46,8,41),(4,45,19,60,14,55,9,50),(5,54,20,49,15,44,10,59),(21,96,36,91,31,86,26,81),(22,85,37,100,32,95,27,90),(23,94,38,89,33,84,28,99),(24,83,39,98,34,93,29,88),(25,92,40,87,35,82,30,97),(61,111,76,106,71,101,66,116),(62,120,77,115,72,110,67,105),(63,109,78,104,73,119,68,114),(64,118,79,113,74,108,69,103),(65,107,80,102,75,117,70,112)]])
C30.D4 is a maximal subgroup of
C40⋊14D6 C40⋊8D6 D40⋊5S3 D30.3D4 D20.34D6 C60.36D4 D20.37D6 D60.C22 D5×D4.S3 D20.9D6 D20.24D6 S3×Q8⋊D5 D20.13D6 D20.D6 D20.28D6
C30.D4 is a maximal quotient of
C30.D8 Dic6⋊Dic5 C30.SD16
Matrix representation of C30.D4 ►in GL6(𝔽241)
| 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 1 | 189 | 0 | 0 |
| 0 | 0 | 0 | 0 | 230 | 192 |
| 0 | 0 | 0 | 0 | 32 | 11 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 20 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 189 | 52 | 0 | 0 |
| 0 | 0 | 240 | 52 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 93 | 240 |
| 77 | 40 | 0 | 0 | 0 | 0 |
| 153 | 164 | 0 | 0 | 0 | 0 |
| 0 | 0 | 189 | 52 | 0 | 0 |
| 0 | 0 | 240 | 52 | 0 | 0 |
| 0 | 0 | 0 | 0 | 51 | 33 |
| 0 | 0 | 0 | 0 | 126 | 228 |
G:=sub<GL(6,GF(241))| [240,0,0,0,0,0,0,240,0,0,0,0,0,0,0,1,0,0,0,0,240,189,0,0,0,0,0,0,230,32,0,0,0,0,192,11],[15,20,0,0,0,0,0,16,0,0,0,0,0,0,189,240,0,0,0,0,52,52,0,0,0,0,0,0,1,93,0,0,0,0,0,240],[77,153,0,0,0,0,40,164,0,0,0,0,0,0,189,240,0,0,0,0,52,52,0,0,0,0,0,0,51,126,0,0,0,0,33,228] >;
C30.D4 in GAP, Magma, Sage, TeX
C_{30}.D_4 % in TeX
G:=Group("C30.D4"); // GroupNames label
G:=SmallGroup(240,16);
// by ID
G=gap.SmallGroup(240,16);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-3,-5,73,55,218,116,50,490,6917]);
// Polycyclic
G:=Group<a,b,c|a^20=b^6=1,c^2=a^15,b*a*b^-1=a^-1,c*a*c^-1=a^9,c*b*c^-1=a^5*b^-1>;
// generators/relations
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Subgroup lattice of C30.D4 in TeX
Character table of C30.D4 in TeX