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D3×D13×C41⋊C5 #44544338

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

Aliases

direct productD3×D13×C41⋊C5
unambiguous semidirect product(D3×C13)⋊(C2×C41⋊C5)
unambiguous semidirect product(C3×D13)⋊(C2×C41⋊C5)
unambiguous semidirect productD39⋊(C2×C41⋊C5)
unambiguous semidirect product(D3×D13×C41)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C41 ⋊ C22×C5
HallC3×C13×C41⋊C5 ⋊ C22
HallD3×D13×C41 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×D3
HallC3×C41⋊C5 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC3×C41 ⋊ C2×C5×D13
SylowC41 ⋊ C5×D3×D13
HallC3×C13 ⋊ C22×C41⋊C5
SylowC13 ⋊ C2×D3×C41⋊C5
SylowC3 ⋊ C2×D13×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C41C22×C5
LCSG ▷ C3×C13×C41
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 66);