Finite Group DatabasebetaFinite Group Databasebeta| order | 24528 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 165888 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C4×C7×C73 |
| multiplicative | (ℤ/37797)ˣ, (ℤ/38193)ˣ, (ℤ/43071)ˣ, (ℤ/46005)ˣ, (ℤ/49064)ˣ, (ℤ/49072)ˣ, (ℤ/50396)ˣ, (ℤ/50924)ˣ, (ℤ/57428)ˣ, (ℤ/61340)ˣ, (ℤ/73596)ˣ, (ℤ/75594)ˣ, (ℤ/76386)ˣ, (ℤ/86142)ˣ, (ℤ/92010)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C23×C3×C7×C73 |
| socle, prime radical | C23×C3×C7×C73 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
216 conjugacy classes of subgroups.
24528 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.