Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#391 ⋊ C4 |
| Sylow | C13 ⋊ #11156 |
826 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^8,13|a^2=g,b^2=h,c^2=d,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^8,c^b=cf,e^b=eh,g^b=gh,g^c=gh,i^g=i^12130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1092924);