Finite Group DatabasebetaFinite Group Databasebeta| order | 10625 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C4×C16×C125 (order 8000) · Inn(G) = C1 · Out(G) = C4×C16×C125 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C10625 |
| abelian | C17×C625 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C125 | C5×C17 |
| socle, prime radical | C5×C17 | C125 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10 conjugacy classes of subgroups.
10625 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic10625, C2×D10625 |
| maximal subgroup of | C2×C17×C625, C3×C17×C625, D10625 |
| maximal normal subgroup of | C2×C17×C625, C3×C17×C625, D10625 |
| maximal quotient of | C2×C17×C625, C3×C17×C625 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10625, 1);