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H(3,𝔽3)⋊#10620321 #31801251

order17739
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C32

Aliases

unambiguous semidirect productH(3,𝔽3)⋊#10620321

Splittings

SylowC73 ⋊ H(3,𝔽3)⋊C9

Subgroups

subgroupG/H
centerC32C32⋊(C73⋊C3)
commutatorC32×C73C3×C9
FrattiniC33C3×C73⋊C3
Fitting, prime radicalC3×H(3,𝔽3)×C73C3
socleC32×C73H(3,𝔽3)
cosocleC33×C73C32
hypercenterC3×H(3,𝔽3)C73⋊C3
hypocenterC73H(3,𝔽3)⋊C9
LCSG ▷ C32×C73 ▷ C3×C73 ▷ C73
UCSC1 ◁ C32 ◁ C33 ◁ C3×H(3,𝔽3)

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5913

Polycyclic presentation:

3^5,73|a^3=d,b^a=bc,c^a=ce,f^a=f^8,c^b=ce

Conjugacy classes & character table

843 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17739, 104);