Finite Group DatabasebetaFinite Group Databasebeta| order | 10125 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5785344000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C53×C9 |
| abelian | C53×C92 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C32×C53 |
| socle, prime radical | C32×C53 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1472 conjugacy classes of subgroups.
10125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C53×C92, C53×C9×C27, C3×C53×C92 |
| maximal normal subgroup of | C2×C53×C92, C53×C9×C27, C3×C53×C92 |
| maximal quotient of | C2×C53×C92, C53×C9×C27, C3×C53×C92 |
Past the SmallGroups library coverage — no SmallGroups id.