Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#1376 ⋊ C2 |
| Sylow | C13 ⋊ #13333 |
546 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 105 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|b^2=h,c^2=h,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,i^a=i^12,c^b=cf,d^b=dg,e^b=eg,f^b=fh,g^b=gh,i^b=i^12,d^c=dg,e^c=eg,f^c=fh,g^c=gh,i^c=i^12376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 88447);