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#131×(C3⋊D3)⋊C3 #13153409

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct product#131×(C3⋊D3)⋊C3

Splittings

FittingH(3,𝔽3)×#131 ⋊ C2
SylowH(3,𝔽3) ⋊ C2×#131

Subgroups

subgroupG/H
centerC8C22×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
FrattiniC3×C4C23×C3×D3
FittingH(3,𝔽3)×#131C2
socleC2×C3C22×C3×C4×D3
prime radical#41×(C3⋊D3)⋊C3C2
cosocleC32×C4C24×C3
hypercenter#131(C3⋊D3)⋊C3
hypocenterC32C2×C3×#131
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ #131

993 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 19472);