Finite Group Databasebeta

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D3×C13×D41⋊C5 #44544328

order31980
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productD3×C13×D41⋊C5
unambiguous semidirect productD41⋊(C5×D3×C13)
unambiguous semidirect product(D3×D41)⋊(C5×C13)
unambiguous semidirect product(C3×D41⋊C5)⋊(C2×C13)
unambiguous semidirect product(D3×C41⋊C5)⋊(C2×C13)
unambiguous semidirect product(C3⋊(D41⋊C5))⋊(C2×C13)
unambiguous semidirect product(D3×C13×D41)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C22×C5
derived, HallC3×C41 ⋊ C22×C5×C13
HallC3×C13×C41⋊C5 ⋊ C22
HallD3×C13×D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×D3
HallC3×C41⋊C5 ⋊ C22×C13
HallC13×C41 ⋊ C2×C5×D3
HallD3×D41 ⋊ C5×C13
HallC41⋊C5 ⋊ C2×D3×C13
SylowC41 ⋊ C2×C5×D3×C13
HallC3×C13 ⋊ C2×D41⋊C5
SylowC3 ⋊ C2×C13×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC13D3×D41⋊C5
commutator, cosocle, hypocenterC3×C41C22×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C41C22×C5
LCSG ▷ C3×C41
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 56);