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C2×C3×D181⋊C5 #24925819

order10860
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D181⋊C5
unambiguous semidirect product(C2×C3×D181)⋊C5

Splittings

Fitting, socleC2×C3×C181 ⋊ C2×C5
derived, SylowC181 ⋊ C22×C3×C5
HallC3×C181⋊C5 ⋊ C22
HallC2×C3×D181 ⋊ C5
HallC181⋊C5 ⋊ C22×C3
HallC2×D181 ⋊ C3×C5
HallC3×C181 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D181⋊C5
commutator, cosocle, hypocenterC181C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C181C2×C5
LCSG ▷ C181
UCSC1 ◁ C2×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(#13108656⋊C2)⋊C5, C2×C9×D181⋊C5, C2×C3×(D181⋊C3)⋊C5, …
maximal normal subgroup ofC2×(#13108656⋊C2)⋊C5, C2×C9×D181⋊C5, C2×C3×(D181⋊C3)⋊C5, …
maximal quotient ofC2×C9×D181⋊C5, C3×D3×D181⋊C5, C2×C32×D181⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 35);