Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C252 · Schur multiplier (H2) = C53×C25 |
| direct product | C25×C52⋊C25 |
| unambiguous semidirect product | C52⋊C252 |
| subgroup | G/H | |
|---|---|---|
| center | C52×C25 | C52 |
| commutator | C5 | C5×C252 |
| Frattini, socle, cosocle | C53 | C53 |
| prime radical | C54 | C52 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C52×C25 ◁ G | |
| LECS | G ▷ C53 ▷ C1 | |
1197 conjugacy classes of subgroups.
3625 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 34);