Finite Group Databasebeta

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Cayley diagram

C3×#4179 #92277

order486
isoclinismisoclinic class of #4179
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C32

Aliases

direct productC3×#4179

Splittings

Fitting, SylowC3×#732 ⋊ C2
derivedC3×C9 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC3#4179
commutator, cosocle, hypocenterC3×C9C2×C32
FrattiniC32C32×D3
FittingC3×#732C2
socleC32(C3⋊D3)⋊C3
LCSG ▷ C3×C9
UCSC1 ◁ C3

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 54

A minimal faithful permutation representation — 2 generators on 30 points:

(4,5,8)(6,24,17,12,13,27)(7,10,18,16,11,23)(9,28,15,19,20,14)(21,29,25,22,30,26);(1,2,3)(4,26,12,16,15,14,7,6,25)(5,13,19,10,22,21,11,9,24)(8,29,27,23,20,28,18,17,30)

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#4178⋊C2, D3×#4179, #4179⋊D3, …
maximal normal subgroup ofC3×#4178⋊C2, D3×#4179, #4179⋊D3, …
maximal quotient ofC3×#66326, C2×C3×#4179, C3×#92160, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 122);