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Dic9×#10597245 #36344796

order21780
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C11

Aliases

direct productDic9×#10597245
unambiguous semidirect productC9⋊(C4×#10597245)

Splittings

derived, HallC9×C112 ⋊ C4×C5
HallC9×#10597245 ⋊ C4
HallC112×Dic9 ⋊ C5
SylowC112 ⋊ C5×Dic9
SylowC9 ⋊ C4×#10597245

Subgroups

subgroupG/H
center, hypercenterC2D9×#10597245
commutator, hypocenterC9×C112C4×C5
FrattiniC2×C3D3×#10597245
Fitting, cosocleC2×C9×C112C2×C5
socleC2×C3×C112C5×D3
prime radicalC2×C3×#10597245D3
LCSG ▷ C9×C112
UCSC1 ◁ C2

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

348 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 145);