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C2×C3×C3⋊((C11⋊C5)⋊D11) #36345233

order21780
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C3⋊((C11⋊C5)⋊D11)
unambiguous semidirect product(C2×C3)⋊(C3×(C11⋊C5)⋊D11)
unambiguous semidirect product(C2×C11⋊C5)⋊(C3×D33)

Splittings

Fitting, socleC2×C32×C112 ⋊ C2×C5
derivedC3×C112 ⋊ C22×C3×C5
HallC32×C11×C11⋊C5 ⋊ C22
HallC2×C3×C3⋊(C11⋊D11) ⋊ C5
HallC32×C112 ⋊ C22×C5
HallC11×C11⋊C5 ⋊ C2×C3×D3
SylowC112 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×(C11⋊C5)⋊D11

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊((C11⋊C5)⋊D11)
commutator, cosocle, hypocenterC3×C112C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C112C2×C5
LCSG ▷ C3×C112
UCSC1 ◁ C2×C3

220 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 60 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

738 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 582);