Finite Group DatabasebetaFinite Group Databasebeta| order | 32400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 225740390400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C33×C5 |
| abelian | C24×C32×C52×C9 |
| multiplicative | (ℤ/45353)ˣ, (ℤ/58311)ˣ, (ℤ/64449)ˣ, (ℤ/90706)ˣ, (ℤ/116622)ˣ, (ℤ/128898)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C24×C33×C52 |
| socle, prime radical | C24×C33×C52 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
26800 conjugacy classes of subgroups.
32400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.