Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 248832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C16×C27 |
| multiplicative | (ℤ/9093)ˣ, (ℤ/9639)ˣ, (ℤ/12124)ˣ, (ℤ/15588)ˣ, (ℤ/18186)ˣ, (ℤ/19278)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C9 | C23×C32 |
| socle, prime radical | C23×C32 | C8×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
686 conjugacy classes of subgroups.
5184 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.