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D3×C13⋊(D31⋊C5) #37563807

order24180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×C13⋊(D31⋊C5)
unambiguous semidirect product(D3×C13)⋊(D31⋊C5)
unambiguous semidirect product(D3×ΓL(1,𝔽32))⋊D13
unambiguous semidirect product(D3×D403)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C31 ⋊ C22×C5
HallC3×C13×ΓL(1,𝔽32) ⋊ C22
HallD3×D403 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×D13
HallC13×C31 ⋊ C2×C5×D3
HallΓL(1,𝔽32) ⋊ D3×D13
HallC3×C31 ⋊ C2×C5×D13
HallC3×C13 ⋊ C2×D31⋊C5
SylowC31 ⋊ C5×D3×D13
SylowC13 ⋊ D3×D31⋊C5
SylowC3 ⋊ C2×C13⋊(D31⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C31C22×C5
LCSG ▷ C3×C13×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 1209

A minimal faithful permutation representation — 2 generators on 47 points:

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

Conjugacy classes & character table

237 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 106);