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C32×(C11⋊C5)⋊D11 #24926148

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

Aliases

direct productC32×(C11⋊C5)⋊D11
unambiguous semidirect product(C11⋊C5)⋊(C32×D11)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC32(C11⋊C5)⋊D11
commutator, cosocle, hypocenterC112C2×C32×C5
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C32

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

414 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×D11×AGL(1,𝔽11), C3×D3×(C11⋊C5)⋊D11, C3×(C3⋊AGL(1,𝔽11))⋊D11, …
maximal normal subgroup ofC32×D11×AGL(1,𝔽11), C3×D3×(C11⋊C5)⋊D11, C3×(C3⋊AGL(1,𝔽11))⋊D11, …
maximal quotient ofC32×(C11⋊C5)⋊Dic11, C2×C32×(C11⋊C5)⋊D11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 97);