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C2×C13⋊(D41⋊C5) #24922504

order10660
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13⋊(D41⋊C5)
unambiguous semidirect product(C2×C13)⋊(D41⋊C5)
unambiguous semidirect product(C2×C41⋊C5)⋊D13
unambiguous semidirect product(C2×D533)⋊C5

Splittings

Fitting, socleC2×C13×C41 ⋊ C2×C5
derived, HallC13×C41 ⋊ C22×C5
HallC13×C41⋊C5 ⋊ C22
HallC2×D533 ⋊ C5
HallC41⋊C5 ⋊ C2×D13
SylowC41 ⋊ C2×C5×D13
SylowC13 ⋊ C2×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C13⋊(D41⋊C5)
commutator, cosocle, hypocenterC13×C41C22×C5
FrattiniC1G
Fitting, socleC2×C13×C41C2×C5
LCSG ▷ C13×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C13⋊C3)⋊(D41⋊C5), D3×C13⋊(D41⋊C5), C2×C3×C13⋊(D41⋊C5), …
maximal normal subgroup ofC2×(C13⋊C3)⋊(D41⋊C5), C2×C3×C13⋊(D41⋊C5)
maximal quotient ofD3×C13⋊(D41⋊C5), C2×C3×C13⋊(D41⋊C5), C2×C3⋊(C13⋊(D41⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10660, 22);