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C3×C4×(C181⋊C3)⋊C5 #45656409

order32580
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×(C181⋊C3)⋊C5
unambiguous semidirect product(C4×C181⋊C3)⋊(C3×C5)
unambiguous semidirect product(C4×C181⋊C5)⋊C32
unambiguous semidirect product(C3×C4×C181⋊C3)⋊C5
unambiguous semidirect product(C3×C4×C181⋊C5)⋊C3

Splittings

FittingC3×C4×C181 ⋊ C3×C5
derived, SylowC181 ⋊ C32×C4×C5
HallC3×C4×C181⋊C3 ⋊ C5
HallC4×C181⋊C5 ⋊ C32
HallC3×C181⋊C3 ⋊ C4×C5
HallC181⋊C5 ⋊ C32×C4
HallC4×C181 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4(C181⋊C3)⋊C5
commutator, hypocenterC181C32×C4×C5
FrattiniC2C2×C3×(C181⋊C3)⋊C5
FittingC3×C4×C181C3×C5
socleC2×C3×C181C2×C3×C5
prime radicalC2×C3×(C181⋊C3)⋊C5C2
cosocleC2×C181C2×C32×C5
LCSG ▷ C181
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

324 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32580, 80);