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Cayley diagram

C3×#4207 #92389

order486
isoclinismisoclinic class of #4207
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C32

Aliases

direct productC3×#4207

Splittings

Fitting, SylowC3×#737 ⋊ C2
derivedC3×C9 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC3#4207
commutator, cosocle, hypocenterC3×C9C2×C32
FrattiniC3C32×C3⋊D3
FittingC3×#737C2
socleC32C3×C3⋊D3
LCSG ▷ C3×C9
UCSC1 ◁ C3

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 30 points:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#4207, C3×#4207⋊C2, #4207⋊D3, …
maximal normal subgroup ofD3×#4207, C3×#4207⋊C2, #4207⋊D3, …
maximal quotient ofC3×#66409, C2×C3×#4207, C3×#92294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 234);