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C2×(C13⋊C3)⋊(D41⋊C5) #44544317

order31980
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C13⋊C3)⋊(D41⋊C5)
unambiguous semidirect product(C2×C13⋊C3)⋊(D41⋊C5)
unambiguous semidirect product(C2×C41⋊C5)⋊(D13⋊C3)
unambiguous semidirect product(C2×(C13⋊C3)⋊D41)⋊C5
unambiguous semidirect product(C2×C13⋊(D41⋊C5))⋊C3

Splittings

Fitting, socleC2×C13×C41 ⋊ C2×C3×C5
derived, HallC13×C41 ⋊ C22×C3×C5
HallC2×C13⋊(D41⋊C5) ⋊ C3
HallC13⋊C3×C41⋊C5 ⋊ C22
HallC2×(C13⋊C3)⋊D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C22×C3
HallC2×D533 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C22×C5
HallC41⋊C5 ⋊ C2×D13⋊C3
SylowC41 ⋊ C2×C5×D13⋊C3
HallC13⋊C3 ⋊ C2×D41⋊C5
SylowC13 ⋊ C2×C3×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2(C13⋊C3)⋊(D41⋊C5)
commutator, cosocle, hypocenterC13×C41C22×C3×C5
FrattiniC1G
Fitting, socleC2×C13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1066

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 45);