Finite Group DatabasebetaFinite Group Databasebeta| order | 6048 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1449197568 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C33 |
| abelian | C23×C33×C4×C7 |
| multiplicative | (ℤ/11739)ˣ, (ℤ/13545)ˣ, (ℤ/15652)ˣ, (ℤ/20124)ˣ, (ℤ/22932)ˣ, (ℤ/23478)ˣ, (ℤ/27090)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C33×C7 |
| socle, prime radical | C24×C33×C7 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
6608 conjugacy classes of subgroups.
6048 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.