Finite Group Databasebeta

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D4×D5×AGL(1,𝔽11) #72276396

order8800
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productD4×D5×AGL(1,𝔽11)

Splittings

FittingC5×D4×C11 ⋊ C22×C5
HallC5×C11⋊C5 ⋊ C22×D4
SylowC11 ⋊ C2×C5×D4×D5

Subgroups

subgroupG/H
center, FrattiniC2C22×D5×AGL(1,𝔽11)
commutator, socle, cosocleC2×C5×C11C24×C5
FittingC5×D4×C11C22×C5
hypercenterD4D5×AGL(1,𝔽11)
hypocenterC5×C11C22×C5×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ D4

1052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×AGL(1,𝔽11)
maximal normal subgroup ofD4×AGL(1,𝔽5)×AGL(1,𝔽11)

GAP

Past the SmallGroups library coverage — no SmallGroups id.