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#10592704⋊C3 #13142698

order1728
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3

Aliases

unambiguous semidirect product#10592704⋊C3

Splittings

FittingH(3,𝔽3)×#117 ⋊ C2
SylowH(3,𝔽3) ⋊ #421

Subgroups

subgroupG/H
centerC4C2×C4⋊((C3⋊D3)⋊C3)
commutatorC32×C4C22×C3×C4
FrattiniC2×C3×C4C22×C3×D3
FittingH(3,𝔽3)×#117C2
socleC2×C3C2×C3×(C2×D3)⋊C4
prime radicalC2×#3828⋊C3C2
cosocleC2×C32×C4C23×C3
hypercenter#117(C3⋊D3)⋊C3
hypocenterC32C3×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

615 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Polycyclic presentation:

2^3,3,2^3,3^2|c^2=e,f^2=g,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,i^a=i^2,c^b=cg,h^d=hi

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8761);