Finite Group Databasebeta

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D4×AGL(1,𝔽5)×D11 #72276328

order3520
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×AGL(1,𝔽5)×D11

Splittings

FittingC5×D4×C11 ⋊ C2×C4
HallC5×C11 ⋊ C2×C4×D4
SylowC11 ⋊ C2×D4×AGL(1,𝔽5)
SylowC5 ⋊ C4×D4×D11

Subgroups

subgroupG/H
center, FrattiniC2C22×AGL(1,𝔽5)×D11
commutator, socleC2×C5×C11C23×C4
FittingC5×D4×C11C2×C4
prime radicalD4×D5×D11C2
cosocleC2×D5×C11C24
hypercenterD4AGL(1,𝔽5)×D11
hypocenterC5×C11C2×C4×D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ D4

852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

175 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.