Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 69672960 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C4×C11×C27 |
| multiplicative | (ℤ/52647)ˣ, (ℤ/58424)ˣ, (ℤ/65205)ˣ, (ℤ/70196)ˣ, (ℤ/86832)ˣ, (ℤ/87636)ˣ, (ℤ/90252)ˣ, (ℤ/96876)ˣ, (ℤ/105294)ˣ, (ℤ/108540)ˣ, (ℤ/130410)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C9 | C24×C32×C11 |
| socle, prime radical | C24×C32×C11 | C2×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3304 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.