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C2×C5×(C11⋊D11)⋊C9 #36344906

order21780
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C5×(C11⋊D11)⋊C9
unambiguous semidirect product(C2×C5×C11⋊D11)⋊C9

Splittings

derived, SylowC112 ⋊ C22×C5×C9
HallC5×C112⋊C9 ⋊ C22
HallC2×C5×C11⋊D11 ⋊ C9
HallC112⋊C9 ⋊ C22×C5
HallC5×C112 ⋊ C22×C9
HallC2×C11⋊D11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5(C11⋊D11)⋊C3
commutator, hypocenterC112C22×C5×C9
FrattiniC3C2×C5×(C11⋊D11)⋊C3
Fitting, socleC2×C3×C5×C112C2×C3
prime radicalC2×C3×C5×C11⋊D11C3
cosocleC3×C112C22×C3×C5
LCSG ▷ C112
UCSC1 ◁ C2×C3×C5

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 255);