Finite Group DatabasebetaFinite Group Databasebeta| order | 21120 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 122880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C5×C11×C32 |
| multiplicative | (ℤ/24541)ˣ, (ℤ/27181)ˣ, (ℤ/32829)ˣ, (ℤ/34947)ˣ, (ℤ/35211)ˣ, (ℤ/42248)ˣ, (ℤ/42368)ˣ, (ℤ/43772)ˣ, (ℤ/46948)ˣ, (ℤ/49082)ˣ, (ℤ/54362)ˣ, (ℤ/63372)ˣ, (ℤ/65658)ˣ, (ℤ/69894)ˣ, (ℤ/70422)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C23×C3×C5×C11 |
| socle, prime radical | C23×C3×C5×C11 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
480 conjugacy classes of subgroups.
21120 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.