Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C8×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #8696 |
384 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 86 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=f,b^2=dh,d^2=g,e^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^8,e^c=egh,f^c=fg,i^c=i^12,i^f=i^12166 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1088755);