Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C54 · Schur multiplier (H2) = C57 |
| direct product | C5×#15691123 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C52 | C5×H(3,𝔽5) |
| commutator, Frattini, cosocle | C52 | C54 |
| LCS | G ▷ C52 ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C52 ◁ C54 ◁ G | |
| LECS | G ▷ C52 ▷ C5 ▷ C1 | |
3672 conjugacy classes of subgroups.
745 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 165);