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Cayley diagram

C3⋊D3×3−1+2 #92388

order486
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3⋊D3×3−1+2
unambiguous semidirect productC3⋊(D3×3−1+2)

Splittings

Fitting, SylowC32×3−1+2 ⋊ C2

Subgroups

subgroupG/H
center, FrattiniC3C32×C3⋊D3
commutator, socle, cosocleC33C2×C32
FittingC32×3−1+2C2
prime radicalC32×C3⋊D3C3
hypercenter3−1+2C3⋊D3
hypocenterC32C2×3−1+2
LCSG ▷ C33 ▷ C32
UCSC1 ◁ C3 ◁ 3−1+2

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 54

A minimal faithful permutation representation — 3 generators on 15 points:

(2,3)(5,6)(8,11,12)(10,14,15);(4,5,6)(7,12,15,9,11,10,13,8,14);(1,2,3)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of3−1+2×#157, 3−1+2⋊#157, D32×3−1+2, …
maximal normal subgroup of3−1+2×#157, 3−1+2⋊#157, D32×3−1+2, …
maximal quotient of3−1+2×C3⋊Dic3, C2×C3⋊D3×3−1+2, C3⋊D3×C32⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 233);