Finite Group Databasebeta

← Prev (#20300071) Next (#20300073) →

C2×C11⋊C5×D33 #20300072

order7260
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊C5×D33
unambiguous semidirect product(C2×C3)⋊(D11×C11⋊C5)

Splittings

Fitting, socleC2×C3×C112 ⋊ C2×C5
derived, HallC3×C112 ⋊ C22×C5
HallC3×C11×C11⋊C5 ⋊ C22
HallC2×C11×D33 ⋊ C5
HallC11×C11⋊C5 ⋊ C2×D3
SylowC112 ⋊ C2×C5×D3
SylowC3 ⋊ C2×D11×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D33
commutator, hypocenterC3×C112C22×C5
FrattiniC1G
Fitting, socleC2×C3×C112C2×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×D99, D3×C11⋊C5×D33, C2×C3×C11⋊C5×D33, …
maximal normal subgroup ofC2×C3×C11⋊C5×D33, C2×C11⋊C5×C3⋊AGL(1,𝔽11), C2×C5×C11⋊C5×D33
maximal quotient ofC2×C11⋊C5×D99, D3×C11⋊C5×D33, C2×C3×C11⋊C5×D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 172);