Finite Group DatabasebetaFinite Group Databasebeta| order | 10125 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 108000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C5 |
| abelian | C5×C25×C81 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C27 | C3×C52 |
| socle, prime radical | C3×C52 | C5×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
70 conjugacy classes of subgroups.
10125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C25×C81, C5×C25×C243, C3×C5×C25×C81 |
| maximal normal subgroup of | C2×C5×C25×C81, C5×C25×C243, C3×C5×C25×C81 |
| maximal quotient of | C2×C5×C25×C81, C5×C25×C243, C3×C5×C25×C81 |
Past the SmallGroups library coverage — no SmallGroups id.