Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #7405 |
252 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 36 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=d,b^2=h,c^2=f,d^2=h,e^2=h,b^a=bc,c^a=ce,e^a=eg,f^a=fh,g^a=gh,i^a=i^8,c^b=cf,d^b=defh,e^b=eh,i^b=i^12,d^c=dgh,e^d=eh,i^d=i^12148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1084506);