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C2×C5⋊((C11⋊D11)⋊C9) #36344908

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

Aliases

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

Splittings

derived, HallC5×C112 ⋊ C22×C9
HallC5×C112⋊C9 ⋊ C22
HallC2×C5⋊(C11⋊D11) ⋊ C9
HallC112⋊C9 ⋊ C2×D5
SylowC112 ⋊ C2×C9×D5
SylowC5 ⋊ C2×(C11⋊D11)⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊((C11⋊D11)⋊C3)
commutator, hypocenterC5×C112C22×C9
FrattiniC3C2×C5⋊((C11⋊D11)⋊C3)
Fitting, socleC2×C3×C5×C112C2×C3
prime radicalC2×C3×C5⋊(C11⋊D11)C3
cosocleC3×C5×C112C22×C3
LCSG ▷ C5×C112
UCSC1 ◁ C2×C3

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

672 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 257);