Finite Group Databasebeta

← Prev (#72248944) Next (#72248946) →

C2×#72222328 #72248945

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

Aliases

direct productC2×#72222328

Splittings

FittingC2×C11×AGL(1,ℤ/8) ⋊ C2×C5
HallC2×#10622811 ⋊ C5
HallC11⋊C5 ⋊ C2×#453
SylowC11 ⋊ C2×C5×#453

Subgroups

subgroupG/H
centerC22#66990⋊C5
commutator, cosocleC2×C4×C11C24×C5
FrattiniC2×C4C23×AGL(1,𝔽11)
FittingC2×C11×AGL(1,ℤ/8)C2×C5
socleC22×C11C5×#120
hypercenterC2×AGL(1,ℤ/8)AGL(1,𝔽11)
hypocenterC11C2×C5×#453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

1688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

182 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.