Finite Group DatabasebetaFinite Group Databasebeta| order | 25625 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C41×C125 ⋊ C5 |
| Sylow | C41 ⋊ C125⋊C5 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5125 |
Polycyclic presentation:
5^4,41|a^5=c,c^5=d,b^a=bd,e^b=e^181145 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25625, 28);