Finite Group Databasebeta

← Prev (#44544334) Next (#44544336) →

D13×C3⋊(D41⋊C5) #44544335

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

Aliases

direct productD13×C3⋊(D41⋊C5)
unambiguous semidirect product(C3×D13)⋊(D41⋊C5)
unambiguous semidirect product(D13×C41⋊C5)⋊D3
unambiguous semidirect product(D13×D123)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C41 ⋊ C22×C5
HallC3×C13×C41⋊C5 ⋊ C22
HallD13×D123 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×D3
HallC3×C41⋊C5 ⋊ C2×D13
HallC13×C41 ⋊ C2×C5×D3
HallC41⋊C5 ⋊ D3×D13
HallC3×C41 ⋊ C2×C5×D13
SylowC41 ⋊ C5×D3×D13
HallC3×C13 ⋊ C2×D41⋊C5
SylowC13 ⋊ C2×C3⋊(D41⋊C5)
SylowC3 ⋊ D13×D41⋊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

minimal degreeμ(G) = 57
transitive degreeμt(G) = 1599

A minimal faithful permutation representation — 2 generators on 57 points:

(2,3)(4,5,7,9,11,13,15,16,14,12,10,8,6)(18,22,23,37,42,19,20,28,30,52)(21,33,34,29,55,25,26,47,39,40)(24,36,35,46,57,27,32,48,49,51)(31,54,38,56,41,44,45,53,43,50);(1,2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,21,27,22,29,41,48,33,47,42,57,32,46,45,53,23,31,30,43,55,40,56,37,44,28,38,54,49,36,51,52,34,26,35,50,39,20,24,25,19)

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 63);