Finite Group DatabasebetaFinite Group Databasebeta| order | 19375 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C25 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C31×C125 ⋊ C5 |
| Sylow | C31 ⋊ C125⋊C5 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3875 |
Polycyclic presentation:
5^4,31|a^5=c,c^5=d,b^a=bd,e^b=e^2895 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19375, 30);