Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C251 ⋊ C2 |
| Sylow | C251 ⋊ #2392 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16064 |
Polycyclic presentation:
2^7,251|a^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^250,c^b=cg,h^b=h^2505044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 7754);