Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#2191 ⋊ C2 |
| Sylow | C13 ⋊ #12172 |
344 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 53 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|c^2=gh,d^2=fh,f^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fh,g^a=gh,d^b=df,e^b=egh,f^b=fh,i^b=i^12,d^c=dg,e^c=eh,i^c=i^12,e^d=eh145 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 82087);