Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C269 ⋊ #2308 |
1160 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 309 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=g,b^a=be,c^a=cf,d^a=de,h^a=h^268,c^b=ce5404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 7088);