Finite Group Databasebeta

#28356729

order13851
automorphism?
homologyAbelianization (H1) = C92 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

FittingC3×C19×C27 ⋊ C9
SylowC19 ⋊ #10624469

Subgroups

subgroupG/H
centerC9C32⋊#4296
commutatorC32×C19C92
FrattiniC3×C9C3×#4296
FittingC3×C19×C27C9
socleC3×C19#6855
prime radicalC32×C19⋊C3C3×C9
cosocleC3×C9×C19⋊C3C32
hypercenterC3×C27#4296
hypocenterC19#10624469
LCSG ▷ C32×C19 ▷ C3×C19 ▷ C19
UCSC1 ◁ C9 ◁ C3×C9 ◁ C3×C27

164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1539

Polycyclic presentation:

3^6,19|a^3=d,b^3=e,e^3=f^2,b^a=bc,c^a=cf,g^a=g^4,g^d=g^7

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 4093);