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Cayley diagram

C3×D27⋊C3 #92268

order486
isoclinismisoclinic class of D27⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×D27⋊C3
unambiguous semidirect productD27⋊C32
unambiguous semidirect product(C3×D27)⋊C3

Splittings

Fitting, SylowC3×C27⋊C3 ⋊ C2
derivedC27 ⋊ C2×C32

Subgroups

subgroupG/H
center, hypercenterC3D27⋊C3
commutator, cosocle, hypocenterC27C2×C32
FrattiniC9C32×D3
FittingC3×C27⋊C3C2
socleC32C3×D9
LCSG ▷ C27
UCSC1 ◁ C3

66 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:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D27⋊C3, C2×C3×D27⋊C3, C9×D27⋊C3, …
maximal normal subgroup ofD3×D27⋊C3, C2×C3×D27⋊C3, C9×D27⋊C3, …
maximal quotient ofC3×(C27⋊C3)⋊C4, C2×C3×D27⋊C3, C3×#6864⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 113);