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#44525135

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

Aliases

No aliases for this group.

Splittings

FittingC3×3−1+2×C127 ⋊ C3
SylowC127 ⋊ #6913

Subgroups

subgroupG/H
centerC3C3×C32⋊(C127⋊C3)
commutator, cosocleC32×C127C33
FrattiniC32C32×C127⋊C3
FittingC3×3−1+2×C127C3
socleC3×C127C3×H(3,𝔽3)
hypercenterC3×3−1+2C127⋊C3
hypocenterC127#6913
LCSG ▷ C32×C127 ▷ C3×C127 ▷ C127
UCSC1 ◁ C3 ◁ C3×C9 ◁ C3×3−1+2

126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3429

Polycyclic presentation:

3^5,127|c^3=e,b^a=bd,d^a=de,f^a=f^107,c^b=ce

Conjugacy classes & character table

1421 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30861, 289);