Finite Group DatabasebetaFinite Group Databasebeta| order | 28512 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 358318080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C33×C4 |
| abelian | C2×C32×C42×C9×C11 |
| multiplicative | (ℤ/32227)ˣ, (ℤ/36127)ˣ, (ℤ/46449)ˣ, (ℤ/64454)ˣ, (ℤ/72254)ˣ, (ℤ/92898)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C3 | C23×C33×C11 |
| socle, prime radical | C23×C33×C11 | C22×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5400 conjugacy classes of subgroups.
28512 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.