Finite Group DatabasebetaFinite Group Databasebeta| order | 9792 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 33030144 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C32×C8×C17 |
| multiplicative | (ℤ/22904)ˣ, (ℤ/23072)ˣ, (ℤ/29448)ˣ, (ℤ/29664)ˣ, (ℤ/34356)ˣ, (ℤ/34524)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4 | C24×C32×C17 |
| socle, prime radical | C24×C32×C17 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2028 conjugacy classes of subgroups.
9792 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.