Finite Group Databasebeta

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#626×AGL(1,𝔽13) #72242016

order11232
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct product#626×AGL(1,𝔽13)

Splittings

HallC32×C13⋊C3 ⋊ C4×D4
SylowC13 ⋊ C3×C4×#626

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D32×AGL(1,𝔽13)
commutator, Fitting, socleC2×C32×C13C22×C3×C4
prime radical#626×D13⋊C3C2
cosocleC2×C32×D13C23×C3
hypocenterC32×C13C3×C4×D4
LCSG ▷ C2×C32×C13 ▷ C32×C13
UCSC1 ◁ C2

1060 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 156

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#3811×AGL(1,𝔽13)
maximal normal subgroup of#3811×AGL(1,𝔽13)

GAP

Past the SmallGroups library coverage — no SmallGroups id.