Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#358 ⋊ C4 |
| Sylow | C13 ⋊ #12939 |
398 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 398 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=f,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^5,d^b=dg,e^b=eg,g^b=gh,i^b=i^8,d^c=dg,e^c=eg,g^c=gh,i^c=i^12,i^f=i^12124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1096979);