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C32×#11925892 #24926141

order10890
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×#11925892

Splittings

Fitting, socle, HallC32×C112 ⋊ C2×C5
derived, SylowC112 ⋊ C2×C32×C5
HallC32×#10597243 ⋊ C2
HallC32×C11⋊D11 ⋊ C5
Hall#10597243 ⋊ C2×C32
HallC11⋊D11 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC32#11925892
commutator, cosocle, hypocenterC112C2×C32×C5
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C32

336 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×#92150⋊C5, C32×#11925892⋊C2, C3×C3⋊(#92150⋊C5), …
maximal normal subgroup ofC32×#92150⋊C5, C32×#11925892⋊C2, C3×C3⋊(#92150⋊C5), …
maximal quotient ofC32×#14559051, C2×C32×#11925892

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 90);