Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #12865 |
334 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^8,13|a^2=f,b^2=g,c^2=d,d^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,c^b=ch,f^b=fh,f^c=fg,i^c=i^12,f^e=fh226 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 85849);