Finite Group DatabasebetaFinite Group Databasebeta| order | 15625 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6250000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25 |
| abelian | C25×C625 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C125 | C52 |
| socle, prime radical | C52 | C5×C125 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C5×C125 ▷ C25 ▷ C5 ▷ C1 | |
107 conjugacy classes of subgroups.
15625 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×C625 |
| maximal normal subgroup of | C2×C25×C625 |
| maximal quotient of | C2×C25×C625 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15625, 3);