Finite Group Databasebeta

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D3×C22⋊(Dic11⋊C5) #72217223

order5280
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productD3×C22⋊(Dic11⋊C5)

Splittings

HallD3×C22⋊Dic11 ⋊ C5
HallC3×C11⋊C5 ⋊ C2×C22⋊C4
HallC11⋊C5 ⋊ D3×C22⋊C4
HallC3×C11 ⋊ C2×C5×C22⋊C4
SylowC11 ⋊ C5×D3×C22⋊C4
SylowC3 ⋊ C2×C22⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, FrattiniC22C2×D3×AGL(1,𝔽11)
commutatorC2×C3×C11C22×C4×C5
FittingC23×C3×C11C22×C5
socle, cosocleC22×C3×C11C23×C5
prime radicalC23×D3×C11⋊C5C2
hypercenterC23D3×AGL(1,𝔽11)
hypocenterC3×C11C2×C5×C22⋊C4
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C22 ◁ C23

528 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C22⋊C4×AGL(1,𝔽11), D3×#67006⋊C5, D3×#66990⋊C5
maximal normal subgroup ofD3×C22⋊C4×AGL(1,𝔽11), D3×#67006⋊C5, D3×#66990⋊C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.