Finite Group DatabasebetaFinite Group Databasebeta| order | 25625 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting | C41×5−1+2 ⋊ C5 |
| Sylow | C41 ⋊ #10597832 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5125 |
Polycyclic presentation:
5^4,41|b^5=d,b^a=bc,c^a=cd,e^a=e^37,e^b=e^10281 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25625, 39);