Finite Group Databasebeta

← Prev (#24926148) Next (#24926150) →

C32×D11×C11⋊C5 #24926149

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

Aliases

direct productC32×D11×C11⋊C5

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, hypercenterC32D11×C11⋊C5
commutator, cosocle, hypocenterC112C2×C32×C5
FrattiniC1G
Fitting, socleC32×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C32

102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

441 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 98);