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D57×D31⋊C5 #47977620

order35340
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD57×D31⋊C5
unambiguous semidirect productD31⋊(C5×D57)
unambiguous semidirect product(C3×D31⋊C5)⋊D19
unambiguous semidirect product(C19×D31⋊C5)⋊D3
unambiguous semidirect product(D31×D57)⋊C5

Splittings

Fitting, socle, derived, HallC3×C19×C31 ⋊ C22×C5
HallC3×C19×ΓL(1,𝔽32) ⋊ C22
HallD31×D57 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×D3
HallC19×C31 ⋊ C2×C5×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×D19
HallΓL(1,𝔽32) ⋊ C2×D57
HallC3×C31 ⋊ C2×C5×D19
HallC3×C19 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×D57
SylowC19 ⋊ D3×D31⋊C5
SylowC3 ⋊ D19×D31⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C19×C31C22×C5
LCSG ▷ C3×C19×C31
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 1767

A minimal faithful permutation representation — 2 generators on 53 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35340, 92);