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D3×C13⋊(D29⋊C7) #44539793

order31668
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productD3×C13⋊(D29⋊C7)
unambiguous semidirect product(D3×C13)⋊(D29⋊C7)
unambiguous semidirect product(D3×C29⋊C7)⋊D13
unambiguous semidirect product(D3×D377)⋊C7

Splittings

Fitting, socle, derived, HallC3×C13×C29 ⋊ C22×C7
HallC3×C13×C29⋊C7 ⋊ C22
HallD3×D377 ⋊ C7
HallC13×C29⋊C7 ⋊ C2×D3
HallC3×C29⋊C7 ⋊ C2×D13
HallC13×C29 ⋊ C2×D3×C7
HallC29⋊C7 ⋊ D3×D13
HallC3×C29 ⋊ C2×C7×D13
HallC3×C13 ⋊ C2×D29⋊C7
SylowC29 ⋊ D3×C7×D13
SylowC13 ⋊ D3×D29⋊C7
SylowC3 ⋊ C2×C13⋊(D29⋊C7)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C29C22×C7
LCSG ▷ C3×C13×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 1131

A minimal faithful permutation representation — 2 generators on 45 points:

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

Conjugacy classes & character table

246 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 88);