Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #3147 |
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16064 |
Polycyclic presentation:
2^7,251|b^2=e,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2508044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 14938);