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C2×C3×D11×C11⋊C5 #20300057

order7260
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D11×C11⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3D11×C11⋊C5
commutator, hypocenterC112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C112C2×C5
LCSG ▷ C112
UCSC1 ◁ C2×C3

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

294 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C9×D11×C11⋊C5, C3×D3×D11×C11⋊C5, C2×C32×D11×C11⋊C5, …
maximal normal subgroup ofC2×C9×D11×C11⋊C5, C2×C32×D11×C11⋊C5, C2×C3×C11⋊C5×AGL(1,𝔽11), …
maximal quotient ofC2×C9×D11×C11⋊C5, C3×D3×D11×C11⋊C5, C2×C32×D11×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7260, 157);