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C2×C3×D3×AGL(1,𝔽13) #72241962

order5616
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C3×D3×AGL(1,𝔽13)

Splittings

Fitting, socleC2×C32×C13 ⋊ C2×C3×C4
derivedC3×C13 ⋊ C22×C32×C4
HallC32×C13⋊C3 ⋊ C22×C4
SylowC13 ⋊ C2×C32×C4×D3

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×AGL(1,𝔽13)
commutator, hypocenterC3×C13C22×C32×C4
FrattiniC1G
Fitting, socleC2×C32×C13C2×C3×C4
prime radicalC2×C3×D3×D13⋊C3C2
cosocleC3×D13C23×C32
LCSG ▷ C3×C13
UCSC1 ◁ C2×C3

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 156

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D32×AGL(1,𝔽13), C3×#67×AGL(1,𝔽13), #626×AGL(1,𝔽13), …
maximal normal subgroup ofC2×D32×AGL(1,𝔽13), C3×#67×AGL(1,𝔽13), #626×AGL(1,𝔽13)
maximal quotient ofC3×#67×AGL(1,𝔽13), C2×AGL(1,ℤ/9)×AGL(1,𝔽13)

GAP

Past the SmallGroups library coverage — no SmallGroups id.