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C9⋊#5465 #13152250

order1728
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C22

Aliases

unambiguous semidirect productC9⋊#5465

Splittings

FittingC9×H(3,𝔽4) ⋊ C3
SylowH(3,𝔽4) ⋊ 3−1+2

Subgroups

subgroupG/H
center, Frattini, socleC22×C3C3×C22⋊A4
commutator, cosocleC3×H(3,𝔽4)C32
FittingC9×H(3,𝔽4)C3
prime radicalC3×#5465C3
hypercenterC22×C9C22⋊A4
hypocenterH(3,𝔽4)3−1+2
LCSG ▷ C3×H(3,𝔽4) ▷ H(3,𝔽4)
UCSC1 ◁ C22×C3 ◁ C22×C9

284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Polycyclic presentation:

3^3,2^6|b^3=c,b^a=bc,d^a=de,e^a=d,f^a=fg,g^a=f,f^d=fi,g^d=ghi,f^e=fh,g^e=gi

Conjugacy classes & character table

89 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18313);