Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C19 ⋊ #11266 |
560 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^8,19|a^2=g,b^2=e,c^2=d,d^2=h,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^18,c^b=cf,d^b=dh,f^b=fh,g^c=gh,i^c=i^18442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 77822);