Finite Group DatabasebetaFinite Group Databasebeta| order | 6250 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 50000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C5 |
| abelian | C2×C5×C625 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C125 | C2×C52 |
| socle | C2×C52 | C125 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
52 conjugacy classes of subgroups.
6250 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C5×C625, C22×C5×C625, C2×C3×C5×C625, … |
| maximal normal subgroup of | C4×C5×C625, C22×C5×C625, C2×C3×C5×C625, … |
| maximal quotient of | C4×C5×C625, C22×C5×C625, C2×C3×C5×C625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6250, 28);