Finite Group DatabasebetaFinite Group Databasebeta| order | 34688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #495×C271 ⋊ C2 |
| Sylow | C271 ⋊ #3156 |
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 17344 |
Polycyclic presentation:
2^7,271|a^2=g,b^2=eg,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^c=h^270,h^d=h^2703002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34688, 15000);