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C5×(C11⋊D11)⋊C9 #24926113

order10890
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C11

Aliases

direct productC5×(C11⋊D11)⋊C9
unambiguous semidirect product(C5×C11⋊D11)⋊C9

Splittings

derived, SylowC112 ⋊ C2×C5×C9
HallC5×C112⋊C9 ⋊ C2
HallC5×C11⋊D11 ⋊ C9
HallC112⋊C9 ⋊ C2×C5
HallC5×C112 ⋊ C2×C9
HallC11⋊D11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5(C11⋊D11)⋊C3
commutator, hypocenterC112C2×C5×C9
FrattiniC3C5×(C11⋊D11)⋊C3
Fitting, socleC3×C5×C112C2×C3
prime radicalC3×C5×C11⋊D11C3
cosocleC3×C112C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C3×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#14546095⋊C2, C5×#17983714, C5×#92150⋊C9, …
maximal normal subgroup ofC5×#14546095⋊C2, C5×#17983714, C5×#92150⋊C9, …
maximal quotient ofC5×(C11⋊Dic11)⋊C9, C2×C5×(C11⋊D11)⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 62);