Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C54 · Schur multiplier (H2) = C54 |
| direct product | C5×#15691109 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C53 | C53 |
| commutator, Frattini, cosocle | C52 | C54 |
| prime radical | C54 | C52 |
| LCS | G ▷ C52 ▷ C1 | |
| UCS | C1 ◁ C53 ◁ G | |
| LECS | G ▷ C52 ▷ C1 | |
1762 conjugacy classes of subgroups.
1225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 102);