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C3×C3⋊#11925890 #24926165

order10890
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊#11925890
unambiguous semidirect productC3⋊(C3×#11925890)

Splittings

Fitting, socle, HallC32×C112 ⋊ D5
derivedC3×#10597245 ⋊ C2×C3
HallC32×#10597245 ⋊ C2
Hall#10597245 ⋊ C3×D3
SylowC112 ⋊ C3×D15
SylowC32 ⋊ #11925890

Subgroups

subgroupG/H
center, hypercenterC3C3⋊#11925890
commutator, cosocle, hypocenterC3×#10597245C2×C3
FrattiniC1G
Fitting, socleC32×C112D5
LCSG ▷ C3×#10597245
UCSC1 ◁ C3

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#11925890⋊D3, C3×#20300024, C3×D3×#11925890, …
maximal normal subgroup ofC3×#11925890⋊D3, C3×#20300024, C3×D3×#11925890, …
maximal quotient ofC3×C3⋊#14559049, C2×C3×C3⋊#11925890

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 114);