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C2×C9×#10597243 #24926118

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

Aliases

direct productC2×C9×#10597243

Splittings

Fitting, HallC2×C9×C112 ⋊ C5
derived, SylowC112 ⋊ C2×C5×C9
HallC9×C112 ⋊ C2×C5
HallC2×C112 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9#10597243
commutator, hypocenterC112C2×C5×C9
FrattiniC3C2×C3×#10597243
FittingC2×C9×C112C5
socleC2×C3×C112C3×C5
prime radicalC2×C3×#10597243C3
cosocleC3×C112C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C2×C9

168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

522 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×#14559051, C9×#14559054, C9⋊#14559051, …
maximal normal subgroup ofC9×#14559051, C9×#14559054, C9⋊#14559051, …
maximal quotient ofC4×C9×#10597243, C22×C9×#10597243

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 67);