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C2×C3⋊(D181⋊C5) #24925820

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

Aliases

direct productC2×C3⋊(D181⋊C5)
unambiguous semidirect product(C2×C3)⋊(D181⋊C5)
unambiguous semidirect product(C2×C181⋊C5)⋊D3
unambiguous semidirect product(C2×D543)⋊C5

Splittings

Fitting, socleC2×C3×C181 ⋊ C2×C5
derived, HallC3×C181 ⋊ C22×C5
HallC3×C181⋊C5 ⋊ C22
HallC2×D543 ⋊ C5
HallC181⋊C5 ⋊ C2×D3
SylowC181 ⋊ C2×C5×D3
SylowC3 ⋊ C2×D181⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(D181⋊C5)
commutator, cosocle, hypocenterC3×C181C22×C5
FrattiniC1G
Fitting, socleC2×C3×C181C2×C5
LCSG ▷ C3×C181
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 36);