Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C55 · Schur multiplier (H2) = C59 |
| direct product | C53×5−1+2 |
| unambiguous semidirect product | C25⋊C54 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C54 | C52 |
| commutator, Frattini, cosocle | C5 | C55 |
| prime radical | C55 | C5 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C54 ◁ G | |
| LECS | G ▷ C5 ▷ C1 | |
51232 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, 39);