Finite Group DatabasebetaFinite Group Databasebeta| order | 24480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 589824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4 |
| abelian | C2×C42×C5×C9×C17 |
| multiplicative | (ℤ/33715)ˣ, (ℤ/45915)ˣ, (ℤ/45975)ˣ, (ℤ/48976)ˣ, (ℤ/61220)ˣ, (ℤ/61300)ˣ, (ℤ/67430)ˣ, (ℤ/91830)ˣ, (ℤ/91950)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C23×C3×C5×C17 |
| socle, prime radical | C23×C3×C5×C17 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
24480 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.