Finite Group Databasebeta

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C22×C9×#10597245 #36344913

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

Aliases

direct productC22×C9×#10597245

Splittings

Fitting, HallC22×C9×C112 ⋊ C5
derived, SylowC112 ⋊ C22×C5×C9
HallC9×C112 ⋊ C22×C5
HallC22×C112 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC22×C9#10597245
commutator, hypocenterC112C22×C5×C9
FrattiniC3C22×C3×#10597245
FittingC22×C9×C112C5
socleC22×C3×C112C3×C5
prime radicalC22×C3×#10597245C3
cosocleC3×C112C22×C3×C5
LCSG ▷ C112
UCSC1 ◁ C22×C9

150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 262);