Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 185794560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C5 |
| abelian | C23×C4×C52×C27 |
| multiplicative | (ℤ/44715)ˣ, (ℤ/47608)ˣ, (ℤ/47696)ˣ, (ℤ/54200)ˣ, (ℤ/59620)ˣ, (ℤ/71412)ˣ, (ℤ/81300)ˣ, (ℤ/89100)ˣ, (ℤ/89430)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C9 | C24×C3×C52 |
| socle, prime radical | C24×C3×C52 | C2×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3776 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.