Finite Group Databasebeta

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#28356036

order13851
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C34

Aliases

No aliases for this group.

Splittings

FittingC9×C19×3−1+2 ⋊ C3
SylowC19 ⋊ #10624879

Subgroups

subgroupG/H
centerC3×C9C32×C19⋊C3
commutator, socle, cosocleC32×C19C34
FrattiniC32C33×C19⋊C3
FittingC9×C19×3−1+2C3
prime radicalC3×C32⋊(C19⋊C3)C32
hypercenterC9×3−1+2C19⋊C3
hypocenterC19#10624879
LCSG ▷ C32×C19 ▷ C19
UCSC1 ◁ C3×C9 ◁ C9×3−1+2

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4617

Polycyclic presentation:

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

Conjugacy classes & character table

747 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13851, 3400);