Finite Group Databasebeta

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#3811×AGL(1,𝔽13) #72242020

order22464
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct product#3811×AGL(1,𝔽13)

Splittings

FittingC22×C32×C13 ⋊ C22×C3×C4
HallC32×C13⋊C3 ⋊ C2×C4×D4
SylowC13 ⋊ C3×C4×#3811

Subgroups

subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽13)
commutator, socleC2×C32×C13C23×C3×C4
FittingC22×C32×C13C22×C3×C4
prime radicalD13⋊C3×#3811C2
cosocleC2×C32×D13C24×C3
hypercenterC22D32×AGL(1,𝔽13)
hypocenterC32×C13C2×C3×C4×D4
LCSG ▷ C2×C32×C13 ▷ C32×C13
UCSC1 ◁ C2 ◁ C22

4364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 156

Conjugacy classes & character table

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

Relationships

holomorph ofDic3×C13, C2×D3×C13

GAP

Past the SmallGroups library coverage — no SmallGroups id.