Finite Group Databasebeta

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C3×C3⋊(#10624382⋊C5) #45656459

order32580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(#10624382⋊C5)
unambiguous semidirect productC3⋊(C3×#10624382⋊C5)
unambiguous semidirect product(C3×C3⋊#10624382)⋊C5

Splittings

Fitting, socle, HallC32×C181 ⋊ C4×C5
derivedC3×C181 ⋊ C3×C4×C5
HallC32×C181⋊C5 ⋊ C4
HallC3×C3⋊#10624382 ⋊ C5
HallC181⋊C5 ⋊ C3×Dic3
SylowC181 ⋊ C3×C5×Dic3
SylowC32 ⋊ #10624382⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(#10624382⋊C5)
commutator, hypocenterC3×C181C3×C4×C5
FrattiniC1G
Fitting, socleC32×C181C4×C5
prime radicalC32×D181⋊C5C2
cosocleC3×D181C2×C3×C5
LCSG ▷ C3×C181
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 130);