Finite Group Databasebeta

← Prev (#72210355) Next (#72210357) →

PGL(2,𝔽13) #72210356

order2184
automorphismAut(G) = PGL(2,𝔽13) (order 2184) · Inn(G) = G · Out(G) = C1
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C2

Aliases

projective general linearPGL(2,𝔽13)

Splittings

socle, derivedPSL(2,𝔽13) ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, socle, cosocle, hypocenterPSL(2,𝔽13)C2
LCSG ▷ PSL(2,𝔽13)
UCSC1

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

(1,14)(3,8)(4,10)(5,11)(6,9)(7,12);(1,2,3,4,5,6,7,8,9,10,11,12,13);(2,8,11,6,10,12,13,7,4,9,5,3)

Conjugacy classes & character table

15 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×PGL(2,𝔽13), C7×PGL(2,𝔽13)
maximal normal subgroup ofC3×PGL(2,𝔽13), C7×PGL(2,𝔽13)
maximal quotient of#72210881, C3×PGL(2,𝔽13), #72234266, …
automorphism group ofPSL(2,𝔽13), Sp(2,𝔽13), PGL(2,𝔽13)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,14)(3,8)(4,10)(5,11)(6,9)(7,12), (1,2,3,4,5,6,7,8,9,10,11,12,13), (2,8,11,6,10,12,13,7,4,9,5,3));