Finite Group DatabasebetaFinite Group Databasebeta| order | 32400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9405849600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C33 |
| abelian | C24×C32×C9×C25 |
| multiplicative | (ℤ/60249)ˣ, (ℤ/80332)ˣ, (ℤ/103284)ˣ, (ℤ/114156)ˣ, (ℤ/120498)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C5 | C24×C33×C5 |
| socle, prime radical | C24×C33×C5 | C3×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10050 conjugacy classes of subgroups.
32400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.