Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C19 ⋊ #7022 |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4864 |
Polycyclic presentation:
2^8,19|a^2=d,b^2=e,c^2=fg,d^2=h,e^2=fh,b^a=bc,c^a=cf,e^a=efg,i^a=i^18,d^b=dg,i^b=i^18568 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 56112);