Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 518366822400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3×C5 |
| abelian | C25×C3×C52×C9 |
| multiplicative | (ℤ/51832)ˣ, (ℤ/73656)ˣ, (ℤ/77748)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C25×C32×C52 |
| socle, prime radical | C25×C32×C52 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
29920 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.