Finite Group Databasebeta

← Prev (#24926088) Next (#24926090) →

C9×#11925894 #24926089

order10890
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#11925894

Splittings

Fitting, HallC9×C112 ⋊ C2×C5
derived, SylowC112 ⋊ C2×C5×C9
HallC9×#10597244 ⋊ C2
HallC9×C11⋊D11 ⋊ C5
Hall#10597244 ⋊ C2×C9
HallC11⋊D11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC9#11925894
commutator, hypocenterC112C2×C5×C9
FrattiniC3C3×#11925894
FittingC9×C112C2×C5
socle, cosocleC3×C112C2×C3×C5
prime radicalC3×#11925894C3
LCSG ▷ C112
UCSC1 ◁ C9

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×#11925894⋊C2, D9×#11925894, #11925894⋊D9, …
maximal normal subgroup ofC9×#11925894⋊C2, D9×#11925894, #11925894⋊D9, …
maximal quotient ofC9×#14559053, C2×C9×#11925894

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 38);