Finite Group Databasebeta

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C32×#11758281 #22579528

order8829
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC32×#11758281
unambiguous semidirect product(C109⋊C3)⋊(C3×C9)

Splittings

Fitting, socleC32×C109 ⋊ C9
derived, SylowC109 ⋊ C32×C9

Subgroups

subgroupG/H
center, hypercenterC32#11758281
commutator, hypocenterC109C32×C9
FrattiniC1G
Fitting, socleC32×C109C9
LCSG ▷ C109
UCSC1 ◁ C32

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C3×#11758281)⋊C9, H(3,𝔽3)⋊#11758281, 3−1+2⋊#11758281, …
maximal normal subgroup of(C3×#11758281)⋊C9, H(3,𝔽3)⋊#11758281, 3−1+2⋊#11758281, …
maximal quotient ofC3×C9×#11758281, C3×C32⋊#11758281, C3×#22579521, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8829, 60);