Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C269 ⋊ #2313 |
512 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 189 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=g,b^2=f,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^268,h^c=h^2683796 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 7112);