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H(3,𝔽3)⋊#11765919 #44525171

order30861
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C32

Aliases

unambiguous semidirect productH(3,𝔽3)⋊#11765919

Splittings

FittingH(3,𝔽3)×C127 ⋊ C9
SylowC127 ⋊ H(3,𝔽3)⋊C9

Subgroups

subgroupG/H
centerC3C32⋊#11765919
commutatorC32×C127C3×C9
FrattiniC32C3×#11765919
FittingH(3,𝔽3)×C127C9
socleC3×C127C32⋊C9
prime radicalH(3,𝔽3)×C127⋊C3C3
cosocleC32×C127⋊C3C32
hypercenterH(3,𝔽3)#11765919
hypocenterC127H(3,𝔽3)⋊C9
LCSG ▷ C32×C127 ▷ C3×C127 ▷ C127
UCSC1 ◁ C3 ◁ C32 ◁ H(3,𝔽3)

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1143

Polycyclic presentation:

3^5,127|a^3=d,b^a=bc,c^a=ce,f^a=f^22,c^b=ce,f^d=f^107

Conjugacy classes & character table

205 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 325);