Finite Group DatabasebetaFinite Group Databasebeta| order | 32400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2149908480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C33×C5 |
| abelian | C22×C32×C4×C52×C9 |
| multiplicative | (ℤ/35929)ˣ, (ℤ/39277)ˣ, (ℤ/50499)ˣ, (ℤ/51057)ˣ, (ℤ/71858)ˣ, (ℤ/78554)ˣ, (ℤ/100998)ˣ, (ℤ/102114)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C23×C33×C52 |
| socle, prime radical | C23×C33×C52 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
10800 conjugacy classes of subgroups.
32400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.