Finite Group Databasebeta

← Prev (#72276367) Next (#72276369) →

C5×C4⋊AGL(1,𝔽11) #72276368

order2200
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×C4⋊AGL(1,𝔽11)

Splittings

FittingC4×C5×C11 ⋊ C2×C5
HallC5×C11⋊C5 ⋊ D4
HallD44 ⋊ C52
SylowC11 ⋊ C52×D4

Subgroups

subgroupG/H
centerC2×C5C2×AGL(1,𝔽11)
commutator, cosocleC2×C11C22×C52
FrattiniC2C2×C5×AGL(1,𝔽11)
FittingC4×C5×C11C2×C5
socleC2×C5×C11C22×C5
hypercenterC4×C5AGL(1,𝔽11)
hypocenterC11C52×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C5 ◁ C4×C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C4⋊AGL(1,𝔽11), C5×D4×AGL(1,𝔽11), #72276389
maximal normal subgroup ofD5×C4⋊AGL(1,𝔽11), C5×D4×AGL(1,𝔽11), #72276389

GAP

Past the SmallGroups library coverage — no SmallGroups id.