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#30633133

order16119
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

No aliases for this group.

Splittings

FittingH(3,𝔽3)×C199 ⋊ C3
SylowC199 ⋊ AΣL(1,𝔽27)

Subgroups

subgroupG/H
centerC3C32⋊(C199⋊C3)
commutator, cosocleC32×C199C32
FrattiniC32C3×C199⋊C3
FittingH(3,𝔽3)×C199C3
socleC3×C199H(3,𝔽3)
hypercenterH(3,𝔽3)C199⋊C3
hypocenterC199AΣL(1,𝔽27)
LCSG ▷ C32×C199 ▷ C3×C199 ▷ C199
UCSC1 ◁ C3 ◁ C32 ◁ H(3,𝔽3)

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1791

Polycyclic presentation:

3^4,199|b^a=bc,c^a=cd,e^b=e^106

Conjugacy classes & character table

743 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16119, 28);