Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C25 · Schur multiplier (H2) = C52 |
| direct product | C5×#15691084 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C52 | C25⋊C25 |
| commutator | C25 | C52×C25 |
| Frattini, cosocle | C5×C25 | C53 |
| prime radical | C53 | 5−1+2 |
| LCS | G ▷ C25 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C52 ◁ C52×C25 ◁ G | |
| LECS | G ▷ C5×C25 ▷ C5 ▷ C1 | |
252 conjugacy classes of subgroups.
745 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 188);