Finite Group DatabasebetaFinite Group Databasebeta| order | 13851 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C19×#6857 ⋊ C3 |
| Sylow | C19 ⋊ #10624595 |
318 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4617 |
Polycyclic presentation:
3^6,19|c^3=e,b^a=bd,c^a=ce,d^a=de,g^a=g^11,d^b=df,g^c=g^7283 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13851, 1129);