Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C53×C25 · Schur multiplier (H2) = C57 |
| direct product | C5×C25×H(3,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center | C52×C25 | C52 |
| commutator | C5 | C53×C25 |
| Frattini, cosocle | C52 | C54 |
| socle | C53 | C53 |
| prime radical | C52×H(3,𝔽5) | C5 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C52×C25 ◁ G | |
| LECS | G ▷ C52 ▷ C1 | |
4622 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, 31);