Finite Group DatabasebetaFinite Group Databasebeta| order | 10625 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C17×C25 · Schur multiplier (H2) = C1 |
| direct product | C17×C125⋊C5 |
| unambiguous semidirect product | C125⋊(C5×C17) |
| unambiguous semidirect product | (C17×C125)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center | C17×C25 | C52 |
| commutator | C5 | C5×C17×C25 |
| Frattini, cosocle | C25 | C52×C17 |
| socle | C5×C17 | C5×C25 |
| prime radical | C52×C17 | C25 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C17×C25 ◁ G | |
32 conjugacy classes of subgroups.
2465 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10625, 6);