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C3×(C181⋊C3)⋊C5 #22550879

order8145
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socleC3×C181 ⋊ C3×C5
derived, SylowC181 ⋊ C32×C5
HallC3×C181⋊C3 ⋊ C5
HallC181⋊C5 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3(C181⋊C3)⋊C5
commutator, hypocenterC181C32×C5
FrattiniC1G
Fitting, socleC3×C181C3×C5
LCSG ▷ C181
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

81 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(D181⋊C3)⋊C5, C3⋊((D181⋊C3)⋊C5), D3×(C181⋊C3)⋊C5, …
maximal normal subgroup ofC3×(D181⋊C3)⋊C5, C3⋊((D181⋊C3)⋊C5), D3×(C181⋊C3)⋊C5, …
maximal quotient ofC2×C3×(C181⋊C3)⋊C5, A4×(C181⋊C3)⋊C5, C3×C22⋊((C181⋊C3)⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8145, 7);