Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C19×#1294 ⋊ C2 |
| Sylow | C19 ⋊ #10394 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^8,19|c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^18,c^b=cf,e^b=eh,i^b=i^18,e^c=eg,i^c=i^18382 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 72839);