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C3×#23779843 #44525092

order30861
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC3×#23779843

Splittings

FittingC3×3−1+2×C127 ⋊ C3
SylowC127 ⋊ C3×AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC32C32⋊(C127⋊C3)
commutator, cosocleC32×C127C33
FrattiniC32C32×C127⋊C3
FittingC3×3−1+2×C127C3
socleC32×C127H(3,𝔽3)
hypercenterC3×3−1+2C127⋊C3
hypocenterC127C3×AΣL(1,𝔽27)
LCSG ▷ C32×C127 ▷ C3×C127 ▷ C127
UCSC1 ◁ C32 ◁ C33 ◁ C3×3−1+2

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3429

Conjugacy classes & character table

1437 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 246);