Finite Group DatabasebetaFinite Group Databasebeta| order | 22500 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1392768000000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C56 |
| abelian | C4×C54×C9 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C2×C3×C54 |
| socle, prime radical | C2×C3×C54 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10080 conjugacy classes of subgroups.
22500 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.