Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Sylow | C19 ⋊ #10624683 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×#4296 |
| commutator, socle | C32×C19 | C32×C9 |
| Fitting, prime radical | C34×C19 | C9 |
| cosocle | C3×#4294 | C33 |
| hypercenter | C34 | #4296 |
| hypocenter | C19 | #10624683 |
| LCS | G ▷ C32×C19 ▷ C19 | |
| UCS | C1 ◁ C32 ◁ C34 | |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^6,19|a^3=e,e^3=f,b^a=bd,c^a=cf,g^a=g^4,g^e=g^7315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 4251);