Finite Group Databasebeta

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C22×C32×D9 #10620103

order648
isoclinismisoclinic class of D9
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3

Aliases

direct productC22×C32×D9

Splittings

FittingC22×C32×C9 ⋊ C2
derivedC9 ⋊ C23×C32
SylowC32×C9 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22×C32D9
commutator, cosocle, hypocenterC9C23×C32
FrattiniC3C22×C32×D3
FittingC22×C32×C9C2
socleC22×C33D3
LCSG ▷ C9
UCSC1 ◁ C22×C32

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(C2×D9)⋊Dic3, (C2×D9)⋊(C3⋊Dic3), C32×(C2×D9)⋊C4, …
maximal normal subgroup ofC3×(C2×D9)⋊Dic3, (C2×D9)⋊(C3⋊Dic3), C32×(C2×D9)⋊C4, …
maximal quotient ofC2×C32×Dic18, C2×C32×C4×D9, C2×C32×D36, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 622);