Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #108×C269 ⋊ C4 |
| Sylow | C269 ⋊ #1383 |
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4304 |
Polycyclic presentation:
2^7,269|a^2=d,b^2=e,c^2=f,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^82,d^b=dg,h^b=h^187,h^d=h^268,h^e=h^268970 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 19576);