Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C38 |
| unambiguous semidirect product | C19⋊#10624562 |
| Fitting | C32×C19×H(3,𝔽3) ⋊ C3 |
| Sylow | C19 ⋊ #10624562 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C32×C19⋊C3 |
| commutator, socle, cosocle | C33×C19 | C33 |
| Fitting | C32×C19×H(3,𝔽3) | C3 |
| hypercenter | C32×H(3,𝔽3) | C19⋊C3 |
| hypocenter | C19 | #10624562 |
| LCS | G ▷ C33×C19 ▷ C19 | |
| UCS | C1 ◁ C33 ◁ C32×H(3,𝔽3) | |
2138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4617 |
Polycyclic presentation:
3^6,19|b^a=bd,c^a=ce,c^b=cf,g^c=g^7699 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 951);