Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D67)⋊C32 |
| Fitting | C67×C22⋊C32 ⋊ C2 |
| Sylow | C67 ⋊ D4×C32 |
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8576 |
Polycyclic presentation:
2^8,67|a^2=e,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bd,i^c=i^662800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 90112);