Finite Group DatabasebetaFinite Group Databasebeta| order | 31584 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11870208 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4×C7×C47 |
| multiplicative | (ℤ/65656)ˣ, (ℤ/68536)ˣ, (ℤ/69195)ˣ, (ℤ/73808)ˣ, (ℤ/92260)ˣ, (ℤ/94896)ˣ, (ℤ/98484)ˣ, (ℤ/102804)ˣ, (ℤ/118620)ˣ, (ℤ/138390)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3×C7×C47 |
| socle, prime radical | C24×C3×C7×C47 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
944 conjugacy classes of subgroups.
31584 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.