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C9×#14559055 #36344779

order21780
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×#14559055

Splittings

derived, SylowC112 ⋊ C4×C5×C9
HallC9×#10597245 ⋊ C4
HallC9×C11×Dic11 ⋊ C5
HallC9×C112 ⋊ C4×C5
Hall#10597245 ⋊ C4×C9
HallC11×Dic11 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9#11925896
commutator, hypocenterC112C4×C5×C9
FrattiniC2×C3C3×#11925896
FittingC2×C9×C112C2×C5
socle, cosocleC2×C3×C112C2×C3×C5
prime radicalC2×C3×#10597245C2×C3
LCSG ▷ C112
UCSC1 ◁ C2×C9

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

450 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 128);