Finite Group DatabasebetaFinite Group Databasebeta| order | 32400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4976640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C5 |
| abelian | C22×C4×C52×C81 |
| multiplicative | (ℤ/44605)ˣ, (ℤ/44825)ˣ, (ℤ/53493)ˣ, (ℤ/60825)ˣ, (ℤ/66825)ˣ, (ℤ/71324)ˣ, (ℤ/81100)ˣ, (ℤ/89210)ˣ, (ℤ/89650)ˣ, (ℤ/106986)ˣ, (ℤ/121650)ˣ, (ℤ/133650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C27 | C23×C3×C52 |
| socle, prime radical | C23×C3×C52 | C2×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1080 conjugacy classes of subgroups.
32400 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.