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Cayley diagram

C3×C9⋊D9 #92289

order486
isoclinismisoclinic class of C9⋊D9
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C9

Aliases

direct productC3×C9⋊D9

Splittings

Fitting, SylowC3×C92 ⋊ C2
derivedC92 ⋊ C2×C3

Subgroups

subgroupG/H
center, hypercenterC3C9⋊D9
commutator, cosocle, hypocenterC92C2×C3
FrattiniC32C3×C3⋊D3
FittingC3×C92C2
socleC33C3⋊D3
LCSG ▷ C92
UCSC1 ◁ C3

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 162

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2,3)(5,7)(6,10)(8,9)(11,12)(14,16)(15,19)(17,18)(20,21);(13,21,16,19,18,17,15,14,20);(4,12,7,10,9,8,6,5,11)

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

derived subgroup of#14517923, #14517928, C3⋊#10619734
maximal subgroup ofC3×#66343, C3⋊#66343, C3×D92, …
maximal normal subgroup ofC3×#66343, C3⋊#66343, C3×D92, …
maximal quotient ofC3×C9⋊Dic9, C2×C3×C9⋊D9, C9×C9⋊D9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 134);