Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C269 ⋊ C2×#324 |
328 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8608 |
Polycyclic presentation:
2^7,269|a^2=e,b^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^187,e^b=ef,h^c=h^268,h^e=h^2681384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 19739);