Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 276480 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3×C4 |
| abelian | C3×C4×C8×C9×C25 |
| multiplicative | (ℤ/22237)ˣ, (ℤ/23413)ˣ, (ℤ/44474)ˣ, (ℤ/46826)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C4×C5 | C22×C32×C5 |
| socle, prime radical | C22×C32×C5 | C2×C3×C4×C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
660 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
| automorphism group of | C37×C601, C13×C1801 |
| outer automorphism group of | C37×C601, C13×C1801 |
Past the SmallGroups library coverage — no SmallGroups id.