Finite Group Databasebeta

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C5×C22⋊(C112⋊C9) #36344949

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

Aliases

direct productC5×C22⋊(C112⋊C9)
unambiguous semidirect productC22⋊(C5×C112⋊C9)
unambiguous semidirect product(C22×C5)⋊(C112⋊C9)
unambiguous semidirect product(C5×C112)⋊(C22⋊C9)

Splittings

derived, HallC22×C112 ⋊ C5×C9
HallC22×C5×C112 ⋊ C9
HallC5×C112 ⋊ C22⋊C9
SylowC112 ⋊ C5×C22⋊C9
HallC22×C5 ⋊ C112⋊C9
SylowC22 ⋊ C5×C112⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C112⋊C3)
commutator, hypocenterC22×C112C5×C9
FrattiniC3C5×C22⋊(C112⋊C3)
Fitting, socle, prime radicalC22×C3×C5×C112C3
cosocleC22×C3×C112C3×C5
LCSG ▷ C22×C112
UCSC1 ◁ C3×C5

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 298);