Finite Group Databasebeta

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C2×#453×AGL(1,𝔽11) #72248985

order14080
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C210

Aliases

direct productC2×#453×AGL(1,𝔽11)

Splittings

FittingC2×C11×#453 ⋊ C2×C5
HallC2×D11×#453 ⋊ C5
HallC11⋊C5 ⋊ C22×#453
SylowC11 ⋊ C22×C5×#453

Subgroups

subgroupG/H
centerC22#120×AGL(1,𝔽11)
commutator, cosocleC2×C4×C11C25×C5
FrattiniC2×C4C24×AGL(1,𝔽11)
FittingC2×C11×#453C2×C5
socleC22×C11C2×C5×#120
hypercenterC2×#453AGL(1,𝔽11)
hypocenterC11C22×C5×#453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#453

11340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

352 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.