Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C54 · Schur multiplier (H2) = C58 |
| direct product | H(3,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C52 | C54 |
| LCS | G ▷ C52 ▷ C1 | |
| UCS | C1 ◁ C52 ◁ G | |
| LECS | G ▷ C52 ▷ C1 | |
5989 conjugacy classes of subgroups.
841 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 240);