Finite Group Databasebeta

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C22×C3×D3×C9 #10620104

order648
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C23×C3

Aliases

direct productC22×C3×D3×C9
unambiguous semidirect productC3⋊(C23×C3×C9)
unambiguous semidirect product(C2×C3)⋊(C22×C3×C9)

Splittings

FittingC22×C32×C9 ⋊ C2
derivedC3 ⋊ C23×C3×C9
SylowC32×C9 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22×C3×C9D3
commutator, hypocenterC3C23×C3×C9
FrattiniC3C22×C32×D3
FittingC22×C32×C9C2
socleC22×C33C2×C3
prime radicalC22×C32×D3C3
cosocleC32C23×C32
LCSG ▷ C3
UCSC1 ◁ C22×C3×C9

395 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

324 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×(C2×D3)⋊Dic9, C9×(C2×D3)⋊Dic3, (C2×D3)⋊(C3⋊Dic9), …
maximal normal subgroup ofC3×(C2×D3)⋊Dic9, C9×(C2×D3)⋊Dic3, (C2×D3)⋊(C3⋊Dic9), …
maximal quotient ofC2×C3×C9×Dic6, C2×C3×C4×D3×C9, C2×C3×C9×D12, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 623);