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D13×ΓL(1,𝔽32) #16860928

order4030
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD13×ΓL(1,𝔽32)
unambiguous semidirect productC13⋊(C2×ΓL(1,𝔽32))
unambiguous semidirect product(D13×C31)⋊C5

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2×C5
HallC13×ΓL(1,𝔽32) ⋊ C2
HallD13×C31 ⋊ C5
SylowC31 ⋊ C5×D13
SylowC13 ⋊ C2×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C31C2×C5
LCSG ▷ C13×C31
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 403

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D13×ΓL(1,𝔽32), D39×ΓL(1,𝔽32), D13×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC3×D13×ΓL(1,𝔽32), D13×(C31⋊C3)⋊C5, D13⋊C3×ΓL(1,𝔽32), …
maximal quotient ofC3×D13×ΓL(1,𝔽32), D39×ΓL(1,𝔽32), D13×C31⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4030, 11);