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C3×C4×C181⋊C5 #24925786

order10860
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC3×C4×C181 ⋊ C5
derived, SylowC181 ⋊ C3×C4×C5
HallC4×C181 ⋊ C3×C5
HallC3×C181 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4C181⋊C5
commutator, hypocenterC181C3×C4×C5
FrattiniC2C2×C3×C181⋊C5
FittingC3×C4×C181C5
socleC2×C3×C181C2×C5
prime radicalC2×C3×C181⋊C5C2
cosocleC2×C181C2×C3×C5
LCSG ▷ C181
UCSC1 ◁ C3×C4

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

492 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C9×C181⋊C5, C4×#13108656⋊C5, C3×C4×(C181⋊C3)⋊C5, …
maximal normal subgroup ofC4×C9×C181⋊C5, C4×#13108656⋊C5, C3×C4×(C181⋊C3)⋊C5, …
maximal quotient ofC4×C9×C181⋊C5, C3×Dic3×C181⋊C5, C32×C4×C181⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 2);