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#38736608

order25029
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

No aliases for this group.

Splittings

FittingAΣL(1,𝔽27)×C103 ⋊ C3
SylowC103 ⋊ #6908

Subgroups

subgroupG/H
centerC3H(3,𝔽3)×C103⋊C3
commutator, cosocleC32×C103C33
FrattiniC32C32×C103⋊C3
FittingAΣL(1,𝔽27)×C103C3
socleC3×C103C3×H(3,𝔽3)
hypercenterAΣL(1,𝔽27)C103⋊C3
hypocenterC103#6908
LCSG ▷ C32×C103 ▷ C3×C103 ▷ C103
UCSC1 ◁ C3 ◁ C32 ◁ AΣL(1,𝔽27)

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2781

Polycyclic presentation:

3^5,103|c^3=e,b^a=bd,d^a=de,f^c=f^56

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25029, 257);