Finite Group Databasebeta

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C3×Dic3⋊AGL(1,𝔽13) #72241996

order5616
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×Dic3⋊AGL(1,𝔽13)

Splittings

HallC32×C13⋊C3 ⋊ C4⋊C4
SylowC13 ⋊ C32×Dic3⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×AGL(1,𝔽13)
commutatorC2×C3×C13C2×C32×C4
FrattiniC2C3×D3×AGL(1,𝔽13)
Fitting, socleC2×C32×C13C2×C3×C4
prime radicalC2×C32×D13⋊C3C22
cosocleC2×C3×D13C22×C32
hypocenterC3×C13C32×C4⋊C4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2×C3

440 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 156

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72242000, C3×#67×AGL(1,𝔽13), #72242017
maximal normal subgroup of#72242000, C3×#67×AGL(1,𝔽13), #72242017

GAP

Past the SmallGroups library coverage — no SmallGroups id.