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C32×#10620323 #20238299

order5913
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC32×#10620323
unambiguous semidirect product(C73⋊C3)⋊(C3×C9)

Splittings

Fitting, socleC32×C73 ⋊ C9
derived, SylowC73 ⋊ C32×C9

Subgroups

subgroupG/H
center, hypercenterC32#10620323
commutator, hypocenterC73C32×C9
FrattiniC1G
Fitting, socleC32×C73C9
LCSG ▷ C73
UCSC1 ◁ C32

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C3×#10620323)⋊C9, H(3,𝔽3)⋊#10620323, 3−1+2⋊#10620323, …
maximal normal subgroup of(C3×#10620323)⋊C9, H(3,𝔽3)⋊#10620323, 3−1+2⋊#10620323, …
maximal quotient ofC3×C9×#10620323, C3×C32⋊#10620323, C3×#20238292, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5913, 60);