Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 13271040 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5 |
| abelian | C2×C42×C52×C27 |
| multiplicative | (ℤ/29755)ˣ, (ℤ/29975)ˣ, (ℤ/40575)ˣ, (ℤ/54100)ˣ, (ℤ/59510)ˣ, (ℤ/59950)ˣ, (ℤ/81150)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C9 | C23×C3×C52 |
| socle, prime radical | C23×C3×C52 | C22×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1728 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.