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G = (C3×C6).F5order 360 = 23·32·5

The non-split extension by C3×C6 of F5 acting via F5/C5=C4

metabelian, soluble, monomial, A-group

Aliases: (C3×C6).F5, (C3×C15)⋊4C8, C5⋊(C322C8), C322(C5⋊C8), C2.(C32⋊F5), (C3×C30).1C4, C10.(C32⋊C4), C3⋊Dic15.1C2, SmallGroup(360,57)

Series: Derived Chief Lower central Upper central

C1C3×C15 — (C3×C6).F5
C1C5C3×C15C3×C30C3⋊Dic15 — (C3×C6).F5
C3×C15 — (C3×C6).F5
C1C2

Generators and relations for (C3×C6).F5
 G = < a,b,c,d | a3=b6=c5=1, d4=b3, ab=ba, ac=ca, dad-1=a-1b2, bc=cb, dbd-1=a-1b, dcd-1=c3 >

2C3
2C3
45C4
2C6
2C6
2C15
2C15
45C8
30Dic3
30Dic3
9Dic5
2C30
2C30
5C3⋊Dic3
9C5⋊C8
6Dic15
6Dic15
5C322C8

Character table of (C3×C6).F5

 class 123A3B4A4B56A6B8A8B8C8D1015A15B15C15D15E15F15G15H30A30B30C30D30E30F30G30H
 size 114445454444545454544444444444444444
ρ1111111111111111111111111111111    trivial
ρ2111111111-1-1-1-111111111111111111    linear of order 2
ρ31111-1-1111-ii-ii11111111111111111    linear of order 4
ρ41111-1-1111i-ii-i11111111111111111    linear of order 4
ρ51-111i-i1-1-1ζ8ζ83ζ85ζ87-111111111-1-1-1-1-1-1-1-1    linear of order 8
ρ61-111-ii1-1-1ζ87ζ85ζ83ζ8-111111111-1-1-1-1-1-1-1-1    linear of order 8
ρ71-111-ii1-1-1ζ83ζ8ζ87ζ85-111111111-1-1-1-1-1-1-1-1    linear of order 8
ρ81-111i-i1-1-1ζ85ζ87ζ8ζ83-111111111-1-1-1-1-1-1-1-1    linear of order 8
ρ9444400-1440000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1    orthogonal lifted from F5
ρ1044-210041-200004-2-2-21111-211-2-2-2-211    orthogonal lifted from C32⋊C4
ρ11441-2004-2100004111-2-2-2-21-2-21111-2-2    orthogonal lifted from C32⋊C4
ρ1244-2100-11-20000-13ζ54+2ζ3ζ5235452+132ζ52+2ζ32ζ532525+13ζ52+2ζ3ζ53525+1ζ3ζ533ζ5253-2ζ52-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ543ζ554-2ζ5-13ζ533ζ52-2ζ5352-13ζ53+2ζ3ζ53535+1ζ3ζ543ζ554-2ζ5-13ζ533ζ52-2ζ5352-13ζ54+2ζ3ζ5235452+13ζ53+2ζ3ζ53535+132ζ52+2ζ32ζ532525+13ζ52+2ζ3ζ53525+1ζ3ζ533ζ5253-2ζ52-1ζ32ζ5432ζ554-2ζ5-1    orthogonal lifted from C32⋊F5
ρ13441-200-1-210000-1ζ3ζ543ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ533ζ52-2ζ5352-13ζ54+2ζ3ζ5235452+132ζ52+2ζ32ζ532525+13ζ52+2ζ3ζ53525+13ζ53+2ζ3ζ53535+1ζ32ζ5432ζ554-2ζ5-13ζ52+2ζ3ζ53525+13ζ53+2ζ3ζ53535+1ζ3ζ543ζ554-2ζ5-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ533ζ52-2ζ5352-13ζ54+2ζ3ζ5235452+132ζ52+2ζ32ζ532525+1    orthogonal lifted from C32⋊F5
ρ1444-2100-11-20000-13ζ52+2ζ3ζ53525+13ζ54+2ζ3ζ5235452+13ζ53+2ζ3ζ53535+1ζ3ζ543ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ533ζ52-2ζ5352-1ζ32ζ5432ζ554-2ζ5-132ζ52+2ζ32ζ532525+13ζ533ζ52-2ζ5352-1ζ32ζ5432ζ554-2ζ5-13ζ52+2ζ3ζ53525+132ζ52+2ζ32ζ532525+13ζ54+2ζ3ζ5235452+13ζ53+2ζ3ζ53535+1ζ3ζ543ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-1    orthogonal lifted from C32⋊F5
ρ15441-200-1-210000-13ζ533ζ52-2ζ5352-1ζ3ζ543ζ554-2ζ5-1ζ32ζ5432ζ554-2ζ5-13ζ52+2ζ3ζ53525+13ζ54+2ζ3ζ5235452+13ζ53+2ζ3ζ53535+132ζ52+2ζ32ζ532525+1ζ3ζ533ζ5253-2ζ52-13ζ53+2ζ3ζ53535+132ζ52+2ζ32ζ532525+13ζ533ζ52-2ζ5352-1ζ3ζ533ζ5253-2ζ52-1ζ3ζ543ζ554-2ζ5-1ζ32ζ5432ζ554-2ζ5-13ζ52+2ζ3ζ53525+13ζ54+2ζ3ζ5235452+1    orthogonal lifted from C32⋊F5
ρ16441-200-1-210000-1ζ32ζ5432ζ554-2ζ5-13ζ533ζ52-2ζ5352-1ζ3ζ533ζ5253-2ζ52-13ζ53+2ζ3ζ53535+13ζ52+2ζ3ζ53525+132ζ52+2ζ32ζ532525+13ζ54+2ζ3ζ5235452+1ζ3ζ543ζ554-2ζ5-132ζ52+2ζ32ζ532525+13ζ54+2ζ3ζ5235452+1ζ32ζ5432ζ554-2ζ5-1ζ3ζ543ζ554-2ζ5-13ζ533ζ52-2ζ5352-1ζ3ζ533ζ5253-2ζ52-13ζ53+2ζ3ζ53535+13ζ52+2ζ3ζ53525+1    orthogonal lifted from C32⋊F5
ρ1744-2100-11-20000-132ζ52+2ζ32ζ532525+13ζ53+2ζ3ζ53535+13ζ54+2ζ3ζ5235452+1ζ32ζ5432ζ554-2ζ5-13ζ533ζ52-2ζ5352-1ζ3ζ533ζ5253-2ζ52-1ζ3ζ543ζ554-2ζ5-13ζ52+2ζ3ζ53525+1ζ3ζ533ζ5253-2ζ52-1ζ3ζ543ζ554-2ζ5-132ζ52+2ζ32ζ532525+13ζ52+2ζ3ζ53525+13ζ53+2ζ3ζ53535+13ζ54+2ζ3ζ5235452+1ζ32ζ5432ζ554-2ζ5-13ζ533ζ52-2ζ5352-1    orthogonal lifted from C32⋊F5
ρ1844-2100-11-20000-13ζ53+2ζ3ζ53535+13ζ52+2ζ3ζ53525+132ζ52+2ζ32ζ532525+13ζ533ζ52-2ζ5352-1ζ3ζ543ζ554-2ζ5-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ54+2ζ3ζ5235452+1ζ32ζ5432ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ53+2ζ3ζ53535+13ζ54+2ζ3ζ5235452+13ζ52+2ζ3ζ53525+132ζ52+2ζ32ζ532525+13ζ533ζ52-2ζ5352-1ζ3ζ543ζ554-2ζ5-1    orthogonal lifted from C32⋊F5
ρ19441-200-1-210000-1ζ3ζ533ζ5253-2ζ52-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ543ζ554-2ζ5-132ζ52+2ζ32ζ532525+13ζ53+2ζ3ζ53535+13ζ54+2ζ3ζ5235452+13ζ52+2ζ3ζ53525+13ζ533ζ52-2ζ5352-13ζ54+2ζ3ζ5235452+13ζ52+2ζ3ζ53525+1ζ3ζ533ζ5253-2ζ52-13ζ533ζ52-2ζ5352-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ543ζ554-2ζ5-132ζ52+2ζ32ζ532525+13ζ53+2ζ3ζ53535+1    orthogonal lifted from C32⋊F5
ρ204-4-21004-120000-4-2-2-21111-2-1-12222-1-1    symplectic lifted from C322C8, Schur index 2
ρ214-4-2100-1-12000013ζ53+2ζ3ζ53535+13ζ52+2ζ3ζ53525+132ζ52+2ζ32ζ532525+13ζ533ζ52-2ζ5352-1ζ3ζ543ζ554-2ζ5-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ54+2ζ3ζ5235452+132ζ5432ζ554+2ζ5+13ζ533ζ5253+2ζ52+13ζ54+2ζ3ζ523545232ζ54+2ζ32ζ523254523ζ54+2ζ3ζ53354533ζ52+2ζ3ζ53525ζ3ζ533ζ52+2ζ5352+13ζ543ζ554+2ζ5+1    symplectic faithful, Schur index 2
ρ224-41-20042-10000-4111-2-2-2-2122-1-1-1-122    symplectic lifted from C322C8, Schur index 2
ρ234-41-200-12-100001ζ3ζ543ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ533ζ52-2ζ5352-13ζ54+2ζ3ζ5235452+132ζ52+2ζ32ζ532525+13ζ52+2ζ3ζ53525+13ζ53+2ζ3ζ53535+1ζ32ζ5432ζ554-2ζ5-13ζ54+2ζ3ζ53354533ζ54+2ζ3ζ52354523ζ543ζ554+2ζ5+132ζ5432ζ554+2ζ5+13ζ533ζ5253+2ζ52+1ζ3ζ533ζ52+2ζ5352+132ζ54+2ζ32ζ523254523ζ52+2ζ3ζ53525    symplectic faithful, Schur index 2
ρ244-41-200-12-100001ζ32ζ5432ζ554-2ζ5-13ζ533ζ52-2ζ5352-1ζ3ζ533ζ5253-2ζ52-13ζ53+2ζ3ζ53535+13ζ52+2ζ3ζ53525+132ζ52+2ζ32ζ532525+13ζ54+2ζ3ζ5235452+1ζ3ζ543ζ554-2ζ5-13ζ52+2ζ3ζ5352532ζ54+2ζ32ζ5232545232ζ5432ζ554+2ζ5+13ζ543ζ554+2ζ5+1ζ3ζ533ζ52+2ζ5352+13ζ533ζ5253+2ζ52+13ζ54+2ζ3ζ52354523ζ54+2ζ3ζ5335453    symplectic faithful, Schur index 2
ρ254-41-200-12-100001ζ3ζ533ζ5253-2ζ52-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ543ζ554-2ζ5-132ζ52+2ζ32ζ532525+13ζ53+2ζ3ζ53535+13ζ54+2ζ3ζ5235452+13ζ52+2ζ3ζ53525+13ζ533ζ52-2ζ5352-132ζ54+2ζ32ζ523254523ζ54+2ζ3ζ53354533ζ533ζ5253+2ζ52+1ζ3ζ533ζ52+2ζ5352+132ζ5432ζ554+2ζ5+13ζ543ζ554+2ζ5+13ζ52+2ζ3ζ535253ζ54+2ζ3ζ5235452    symplectic faithful, Schur index 2
ρ264-4-2100-1-12000013ζ54+2ζ3ζ5235452+132ζ52+2ζ32ζ532525+13ζ52+2ζ3ζ53525+1ζ3ζ533ζ5253-2ζ52-1ζ32ζ5432ζ554-2ζ5-1ζ3ζ543ζ554-2ζ5-13ζ533ζ52-2ζ5352-13ζ53+2ζ3ζ53535+13ζ543ζ554+2ζ5+1ζ3ζ533ζ52+2ζ5352+132ζ54+2ζ32ζ523254523ζ54+2ζ3ζ52354523ζ52+2ζ3ζ535253ζ54+2ζ3ζ53354533ζ533ζ5253+2ζ52+132ζ5432ζ554+2ζ5+1    symplectic faithful, Schur index 2
ρ274-4-2100-1-120000132ζ52+2ζ32ζ532525+13ζ53+2ζ3ζ53535+13ζ54+2ζ3ζ5235452+1ζ32ζ5432ζ554-2ζ5-13ζ533ζ52-2ζ5352-1ζ3ζ533ζ5253-2ζ52-1ζ3ζ543ζ554-2ζ5-13ζ52+2ζ3ζ53525+13ζ533ζ5253+2ζ52+13ζ543ζ554+2ζ5+13ζ52+2ζ3ζ535253ζ54+2ζ3ζ53354533ζ54+2ζ3ζ523545232ζ54+2ζ32ζ5232545232ζ5432ζ554+2ζ5+1ζ3ζ533ζ52+2ζ5352+1    symplectic faithful, Schur index 2
ρ284-4-2100-1-12000013ζ52+2ζ3ζ53525+13ζ54+2ζ3ζ5235452+13ζ53+2ζ3ζ53535+1ζ3ζ543ζ554-2ζ5-1ζ3ζ533ζ5253-2ζ52-13ζ533ζ52-2ζ5352-1ζ32ζ5432ζ554-2ζ5-132ζ52+2ζ32ζ532525+1ζ3ζ533ζ52+2ζ5352+132ζ5432ζ554+2ζ5+13ζ54+2ζ3ζ53354533ζ52+2ζ3ζ5352532ζ54+2ζ32ζ523254523ζ54+2ζ3ζ52354523ζ543ζ554+2ζ5+13ζ533ζ5253+2ζ52+1    symplectic faithful, Schur index 2
ρ294-44400-1-4-400001-1-1-1-1-1-1-1-111111111    symplectic lifted from C5⋊C8, Schur index 2
ρ304-41-200-12-1000013ζ533ζ52-2ζ5352-1ζ3ζ543ζ554-2ζ5-1ζ32ζ5432ζ554-2ζ5-13ζ52+2ζ3ζ53525+13ζ54+2ζ3ζ5235452+13ζ53+2ζ3ζ53535+132ζ52+2ζ32ζ532525+1ζ3ζ533ζ5253-2ζ52-13ζ54+2ζ3ζ52354523ζ52+2ζ3ζ53525ζ3ζ533ζ52+2ζ5352+13ζ533ζ5253+2ζ52+13ζ543ζ554+2ζ5+132ζ5432ζ554+2ζ5+13ζ54+2ζ3ζ533545332ζ54+2ζ32ζ52325452    symplectic faithful, Schur index 2

Smallest permutation representation of (C3×C6).F5
On 120 points
Generators in S120
(2 51 12)(4 14 53)(6 55 16)(8 10 49)(17 29 106)(19 108 31)(21 25 110)(23 112 27)(34 114 80)(36 74 116)(38 118 76)(40 78 120)(42 104 59)(44 61 98)(46 100 63)(48 57 102)(65 95 87)(67 81 89)(69 91 83)(71 85 93)
(1 15 50 5 11 54)(2 16 51 6 12 55)(3 56 13 7 52 9)(4 49 14 8 53 10)(17 110 29 21 106 25)(18 26 107 22 30 111)(19 27 108 23 31 112)(20 105 32 24 109 28)(33 75 113 37 79 117)(34 76 114 38 80 118)(35 119 73 39 115 77)(36 120 74 40 116 78)(41 62 103 45 58 99)(42 63 104 46 59 100)(43 101 60 47 97 64)(44 102 61 48 98 57)(65 83 95 69 87 91)(66 92 88 70 96 84)(67 93 81 71 89 85)(68 86 90 72 82 94)
(1 99 88 113 28)(2 114 100 29 81)(3 30 115 82 101)(4 83 31 102 116)(5 103 84 117 32)(6 118 104 25 85)(7 26 119 86 97)(8 87 27 98 120)(9 22 39 72 43)(10 65 23 44 40)(11 45 66 33 24)(12 34 46 17 67)(13 18 35 68 47)(14 69 19 48 36)(15 41 70 37 20)(16 38 42 21 71)(49 95 112 61 78)(50 62 96 79 105)(51 80 63 106 89)(52 107 73 90 64)(53 91 108 57 74)(54 58 92 75 109)(55 76 59 110 93)(56 111 77 94 60)
(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)

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

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

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

Matrix representation of (C3×C6).F5 in GL4(𝔽241) generated by

1000
0100
0014784
0015793
,
9415700
8414800
0014884
0015794
,
5124000
1000
00190190
0051240
,
0010
0001
18311300
475800
G:=sub<GL(4,GF(241))| [1,0,0,0,0,1,0,0,0,0,147,157,0,0,84,93],[94,84,0,0,157,148,0,0,0,0,148,157,0,0,84,94],[51,1,0,0,240,0,0,0,0,0,190,51,0,0,190,240],[0,0,183,47,0,0,113,58,1,0,0,0,0,1,0,0] >;

(C3×C6).F5 in GAP, Magma, Sage, TeX

(C_3\times C_6).F_5
% in TeX

G:=Group("(C3xC6).F5");
// GroupNames label

G:=SmallGroup(360,57);
// by ID

G=gap.SmallGroup(360,57);
# by ID

G:=PCGroup([6,-2,-2,-2,-3,3,-5,12,31,1347,201,1924,730,5189,5195]);
// Polycyclic

G:=Group<a,b,c,d|a^3=b^6=c^5=1,d^4=b^3,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1*b^2,b*c=c*b,d*b*d^-1=a^-1*b,d*c*d^-1=c^3>;
// generators/relations

Export

Subgroup lattice of (C3×C6).F5 in TeX
Character table of (C3×C6).F5 in TeX

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