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C22×(C181⋊C3)⋊C5 #24925809

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

Aliases

direct productC22×(C181⋊C3)⋊C5
unambiguous semidirect product(C22×C181⋊C3)⋊C5

Splittings

Fitting, socle, HallC22×C181 ⋊ C3×C5
derived, SylowC181 ⋊ C22×C3×C5
HallC22×C181⋊C5 ⋊ C3
HallC22×C181⋊C3 ⋊ C5
HallC181⋊C5 ⋊ C22×C3
HallC181⋊C3 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC22(C181⋊C3)⋊C5
commutator, cosocle, hypocenterC181C22×C3×C5
FrattiniC1G
Fitting, socleC22×C181C3×C5
LCSG ▷ C181
UCSC1 ◁ C22

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22⋊(#13108658⋊C5), A4×(C181⋊C3)⋊C5, C22×#13108658⋊C5, …
maximal normal subgroup ofC22⋊(#13108658⋊C5), A4×(C181⋊C3)⋊C5, C22×#13108658⋊C5, …
maximal quotient ofC22×#13108656⋊C5, C2×D3×(C181⋊C3)⋊C5, C22×C3×(C181⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 25);