Finite Group DatabasebetaFinite Group Databasebeta| order | 8125 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C3×C42×C125 (order 6000) · Inn(G) = C1 · Out(G) = C3×C42×C125 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C8125 |
| abelian | C13×C625 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C125 | C5×C13 |
| socle | C5×C13 | C125 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10 conjugacy classes of subgroups.
8125 conjugacy classes. The character table is too large to display.
| derived subgroup of | Dic8125, C2×D8125 |
| maximal subgroup of | C2×C13×C625, C3×C13×C625, D8125 |
| maximal normal subgroup of | C2×C13×C625, C3×C13×C625, D8125 |
| maximal quotient of | C2×C13×C625, C3×C13×C625 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8125, 1);