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D3×C13⋊(D41⋊C5) #44544336

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

Aliases

direct productD3×C13⋊(D41⋊C5)
unambiguous semidirect product(D3×C13)⋊(D41⋊C5)
unambiguous semidirect product(D3×C41⋊C5)⋊D13
unambiguous semidirect product(D3×D533)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C41 ⋊ C22×C5
HallC3×C13×C41⋊C5 ⋊ C22
HallD3×D533 ⋊ 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 ⋊ D3×D41⋊C5
SylowC3 ⋊ C2×C13⋊(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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 64);