Finite Group Databasebeta

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C3×#10597729⋊C3 #72242002

order5616
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×#10597729⋊C3

Splittings

FittingC22×C32×C13 ⋊ C3×C4
HallC32×C13⋊C3 ⋊ C22⋊C4
SylowC13 ⋊ C32×#217

Subgroups

subgroupG/H
centerC2×C3C2×C3⋊AGL(1,𝔽13)
commutatorC2×C3×C13C2×C32×C4
FrattiniC2C2×C3×C3⋊AGL(1,𝔽13)
FittingC22×C32×C13C3×C4
socleC2×C32×C13C2×C3×C4
prime radicalC22×C32×D13⋊C3C2
cosocleC2×C3×D13C22×C32
hypercenterC22×C3C3⋊AGL(1,𝔽13)
hypocenterC3×C13C32×C22⋊C4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2×C3 ◁ C22×C3

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 156

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72242005, C3×#67×AGL(1,𝔽13), #72242015
maximal normal subgroup of#72242005, C3×#67×AGL(1,𝔽13), #72242015

GAP

Past the SmallGroups library coverage — no SmallGroups id.