Finite Group DatabasebetaFinite Group Databasebeta| order | 24912 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1585152 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C32×C4×C173 |
| multiplicative | (ℤ/31577)ˣ, (ℤ/36365)ˣ, (ℤ/40521)ˣ, (ℤ/40599)ˣ, (ℤ/46755)ˣ, (ℤ/54028)ˣ, (ℤ/63154)ˣ, (ℤ/72730)ˣ, (ℤ/81042)ˣ, (ℤ/81198)ˣ, (ℤ/93510)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C32×C173 |
| socle, prime radical | C23×C32×C173 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
324 conjugacy classes of subgroups.
24912 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.