Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #336×C269 ⋊ C2 |
| Sylow | C269 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17216 |
Polycyclic presentation:
2^7,269|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,h^c=h^2685440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 4267);