Finite Group DatabasebetaFinite Group Databasebeta| order | 32400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3135283200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3×C5 |
| abelian | C24×C3×C52×C27 |
| multiplicative | (ℤ/62601)ˣ, (ℤ/67208)ˣ, (ℤ/83468)ˣ, (ℤ/100812)ˣ, (ℤ/107316)ˣ, (ℤ/110484)ˣ, (ℤ/125202)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C9 | C24×C32×C52 |
| socle, prime radical | C24×C32×C52 | C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7504 conjugacy classes of subgroups.
32400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.