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C4×(C181⋊C3)⋊C5 #24925788

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

Aliases

direct productC4×(C181⋊C3)⋊C5
unambiguous semidirect product(C4×C181⋊C3)⋊C5
unambiguous semidirect product(C4×C181⋊C5)⋊C3

Splittings

Fitting, HallC4×C181 ⋊ C3×C5
derived, SylowC181 ⋊ C3×C4×C5
HallC4×C181⋊C5 ⋊ C3
HallC4×C181⋊C3 ⋊ C5
HallC181⋊C5 ⋊ C3×C4
HallC181⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC4(C181⋊C3)⋊C5
commutator, hypocenterC181C3×C4×C5
FrattiniC2C2×(C181⋊C3)⋊C5
FittingC4×C181C3×C5
socle, cosocleC2×C181C2×C3×C5
prime radicalC2×(C181⋊C3)⋊C5C2
LCSG ▷ C181
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#13108658⋊C5, Dic3×(C181⋊C3)⋊C5, C3×C4×(C181⋊C3)⋊C5
maximal normal subgroup ofC4×#13108658⋊C5, C3×C4×(C181⋊C3)⋊C5
maximal quotient ofC4×#13108656⋊C5, Dic3×(C181⋊C3)⋊C5, C3×C4×(C181⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 4);