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D13⋊C3×D41⋊C5 #44544315

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

Aliases

direct productD13⋊C3×D41⋊C5
unambiguous semidirect productD13⋊(C3×D41⋊C5)
unambiguous semidirect productD41⋊(C5×D13⋊C3)
unambiguous semidirect product(D13⋊C3×D41)⋊C5
unambiguous semidirect product(D13×D41⋊C5)⋊C3
unambiguous semidirect product(C13⋊C3×D41⋊C5)⋊C2
unambiguous semidirect product(D13⋊C3×C41⋊C5)⋊C2
unambiguous semidirect product((C13⋊C3)⋊(D41⋊C5))⋊C2

Splittings

Fitting, socle, derived, HallC13×C41 ⋊ C22×C3×C5
HallD13×D41⋊C5 ⋊ C3
HallC13⋊C3×C41⋊C5 ⋊ C22
HallD13⋊C3×D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C22×C3
HallD13×D41 ⋊ 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, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C41C22×C3×C5
LCSG ▷ C13×C41
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 533

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 43);