Finite Group DatabasebetaFinite Group Databasebeta| order | 24624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 80621568 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33 |
| abelian | C22×C32×C4×C9×C19 |
| multiplicative | (ℤ/30457)ˣ, (ℤ/32851)ˣ, (ℤ/39159)ˣ, (ℤ/42237)ˣ, (ℤ/43281)ˣ, (ℤ/60914)ˣ, (ℤ/65702)ˣ, (ℤ/78318)ˣ, (ℤ/84474)ˣ, (ℤ/86562)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C33×C19 |
| socle, prime radical | C23×C33×C19 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2700 conjugacy classes of subgroups.
24624 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.