Finite Group DatabasebetaFinite Group Databasebeta| order | 32400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 207360 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C25×C81 |
| multiplicative | (ℤ/49389)ˣ, (ℤ/60765)ˣ, (ℤ/61125)ˣ, (ℤ/64808)ˣ, (ℤ/64816)ˣ, (ℤ/65852)ˣ, (ℤ/81020)ˣ, (ℤ/81500)ˣ, (ℤ/97212)ˣ, (ℤ/98172)ˣ, (ℤ/98778)ˣ, (ℤ/121500)ˣ, (ℤ/121530)ˣ, (ℤ/122250)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C5×C27 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C2×C5×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
405 conjugacy classes of subgroups.
32400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.