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C22×C3×(C112⋊C3)⋊C5 #36345177

order21780
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×(C112⋊C3)⋊C5
unambiguous semidirect product(C22×C3×C112⋊C3)⋊C5

Splittings

Fitting, socleC22×C3×C112 ⋊ C3×C5
derived, SylowC112 ⋊ C22×C32×C5
HallC22×C3×C112⋊C3 ⋊ C5
HallC22×#10597243 ⋊ C32
HallC3×C112⋊C3 ⋊ C22×C5
Hall#10597243 ⋊ C22×C32
HallC22×C112 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC22×C3(C112⋊C3)⋊C5
commutator, cosocle, hypocenterC112C22×C32×C5
FrattiniC1G
Fitting, socleC22×C3×C112C3×C5
LCSG ▷ C112
UCSC1 ◁ C22×C3

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 526);