Finite Group Databasebeta

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C3×C3⋊#14559053 #36344985

order21780
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊#14559053
unambiguous semidirect productC3⋊(C3×#14559053)

Splittings

derivedC3×C112 ⋊ C3×C4×C5
HallC32×#10597244 ⋊ C4
HallC3×C3⋊(C11⋊Dic11) ⋊ C5
HallC32×C112 ⋊ C4×C5
Hall#10597244 ⋊ C3×Dic3
SylowC112 ⋊ C3×C5×Dic3
SylowC32 ⋊ #14559053

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊#11925894
commutator, hypocenterC3×C112C3×C4×C5
FrattiniC2C3×C3⋊#11925894
Fitting, socleC2×C32×C112C2×C5
prime radicalC2×C32×#10597244C2
cosocleC2×C3×C112C2×C3×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2×C3

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

306 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 334);