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C3×Dic3×AΓL(1,𝔽9) #72259682

order5184
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×Dic3×AΓL(1,𝔽9)

Splittings

SylowC34 ⋊ C4×SD16

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×AΓL(1,𝔽9)
commutatorC3×#157C22×C3×C4
FrattiniC2C3×D3×AΓL(1,𝔽9)
Fitting, socleC2×C34C2×SD16
prime radicalC2×C32×GO+(4,𝔽2)C22
cosocleC2×C3×#157C23×C3
hypocenterC33C3×C4×SD16
LCSG ▷ C3×#157 ▷ C3×C3⋊D3 ▷ C33
UCSC1 ◁ C2×C3

769 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×Dic3×AGL(2,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.