Finite Group Databasebeta

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C22×((C2×D11)⋊C4)⋊C5 #72248865

order3520
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct productC22×((C2×D11)⋊C4)⋊C5

Splittings

FittingC23×C4×C11 ⋊ C2×C5
HallC22×(C2×D11)⋊C4 ⋊ C5
HallC11⋊C5 ⋊ C22×C22⋊C4
SylowC11 ⋊ C22×C5×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×AGL(1,𝔽11)
commutatorC2×C11C23×C4×C5
FrattiniC22C23×AGL(1,𝔽11)
FittingC23×C4×C11C2×C5
socleC24×C11C22×C5
prime radicalC24×AGL(1,𝔽11)C2
cosocleC22×C11C24×C5
hypercenterC23×C4AGL(1,𝔽11)
hypocenterC11C22×C5×C22⋊C4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4

1348 conjugacy classes of subgroups; only the 416 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 416 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 352

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C22⋊C4×AGL(1,𝔽11), C22×#66990⋊C5, C22×#66935⋊C5
maximal normal subgroup ofC22×C22⋊C4×AGL(1,𝔽11), C22×#66990⋊C5, C22×#66935⋊C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.