Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C269 ⋊ #1291 |
138 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 44 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=d,b^2=e,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^187,h^e=h^2681372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 19376);