Finite Group DatabasebetaFinite Group Databasebeta| order | 34432 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C269 ⋊ C4 |
| Sylow | C269 ⋊ #1304 |
396 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 48 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,b^a=bc,c^a=cf,e^a=eg,h^a=h^187,c^b=cg,d^b=df,h^d=h^2681366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34432, 19409);