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AGL(1,𝔽13)×C41⋊C5 #44544313

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽13)×C41⋊C5
unambiguous semidirect product#261⋊(C3×C41⋊C5)
unambiguous semidirect product(C41×AGL(1,𝔽13))⋊C5
unambiguous semidirect product(#261×C41⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC13×C41 ⋊ C3×C4×C5
Hall#261×C41⋊C5 ⋊ C3
HallC13⋊C3×C41⋊C5 ⋊ C4
HallC41×AGL(1,𝔽13) ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
HallC41×#261 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
Hall#261 ⋊ C3×C41⋊C5
SylowC41 ⋊ C5×AGL(1,𝔽13)
HallC13⋊C3 ⋊ C4×C41⋊C5
SylowC13 ⋊ C3×C4×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C41C3×C4×C5
prime radicalD13⋊C3×C41⋊C5C2
cosocleD13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 533

Conjugacy classes & character table

169 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 41);