Finite Group Databasebeta

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Cayley diagram

C3×#4177 #92274

order486
isoclinismisoclinic class of #4177
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C32

Aliases

direct productC3×#4177

Splittings

Fitting, SylowC3×#731 ⋊ C2
derivedC3×C9 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC3#4177
commutator, cosocle, hypocenterC3×C9C2×C32
FrattiniC32C32×D3
FittingC3×#731C2
socleC32(C3⋊D3)⋊C3
LCSG ▷ C3×C9
UCSC1 ◁ C3

78 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)(6,21,17,12,13,27)(7,10,18,16,11,23)(9,29,15,19,20,26)(14,22,28,24,25,30);(1,2,3)(4,15,12,7,24,14,16,6,26)(5,22,19,11,13,21,10,9,25)(8,20,27,18,30,28,23,17,29)

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#4176⋊C2, D3×#4177, #4177⋊D3, …
maximal normal subgroup ofC3×#4176⋊C2, D3×#4177, #4177⋊D3, …
maximal quotient ofC3×#66324, C2×C3×#4177, C3×#92161, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 119);