Finite Group Databasebeta

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C2×C11⋊C5×#453 #72248935

order7040
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC2×C11⋊C5×#453

Splittings

Fitting, HallC2×C11×#453 ⋊ C5
SylowC11 ⋊ C2×C5×#453

Subgroups

subgroupG/H
centerC22#120×C11⋊C5
commutator, cosocleC2×C4×C11C24×C5
FrattiniC2×C4C24×C11⋊C5
FittingC2×C11×#453C5
socleC22×C11C5×#120
hypercenterC2×#453C11⋊C5
hypocenterC11C2×C5×#453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#453

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#453×AGL(1,𝔽11)
maximal normal subgroup ofC2×#453×AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.