Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C54 · Schur multiplier (H2) = C56 |
| direct product | C5×#15691122 |
| subgroup | G/H | |
|---|---|---|
| center | C5×C25 | H(3,𝔽5) |
| commutator, Frattini, cosocle | C52 | C54 |
| socle | C52 | C5×H(3,𝔽5) |
| prime radical | C5×H(3,𝔽5)⋊C5 | C5 |
| LCS | G ▷ C52 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C25 ◁ C52×C25 ◁ G | |
| LECS | G ▷ C52 ▷ C5 ▷ C1 | |
2642 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, 47);