Finite Group Databasebeta

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C11⋊C5×C4⋊AGL(1,𝔽5) #72276404

order4400
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC11⋊C5×C4⋊AGL(1,𝔽5)

Splittings

FittingC4×C5×C11 ⋊ C4×C5
HallC5×C11⋊C5 ⋊ C4⋊C4
SylowC11 ⋊ C5×C4⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, FrattiniC2C2×AGL(1,𝔽5)×C11⋊C5
commutator, socleC2×C5×C11C2×C4×C5
FittingC4×C5×C11C4×C5
prime radicalC2×D5×C11⋊C5C22
cosocleC2×D5×C11C22×C5
hypercenterC4AGL(1,𝔽5)×C11⋊C5
hypocenterC5×C11C5×C4⋊C4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C4

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×AGL(1,𝔽5)×C11⋊C5, C4⋊AGL(1,𝔽5)×AGL(1,𝔽11), #72276420
maximal normal subgroup ofD4×AGL(1,𝔽5)×C11⋊C5, C4⋊AGL(1,𝔽5)×AGL(1,𝔽11), #72276420

GAP

Past the SmallGroups library coverage — no SmallGroups id.