Finite Group Databasebeta

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C3×#67×AGL(1,𝔽13) #72242013

order11232
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC3×#67×AGL(1,𝔽13)

Splittings

FittingC22×C32×C13 ⋊ C2×C3×C4
HallC32×C13⋊C3 ⋊ C4×D4
SylowC13 ⋊ C32×C4×#67

Subgroups

subgroupG/H
centerC2×C3C2×D3×AGL(1,𝔽13)
commutatorC2×C3×C13C22×C32×C4
FrattiniC2C2×C3×D3×AGL(1,𝔽13)
FittingC22×C32×C13C2×C3×C4
socleC2×C32×C13C22×C3×C4
prime radicalC3×#67×D13⋊C3C2
cosocleC2×C3×D13C23×C32
hypercenterC22×C3D3×AGL(1,𝔽13)
hypocenterC3×C13C32×C4×D4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2×C3 ◁ C22×C3

1560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 156

Conjugacy classes & character table

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

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.