Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 19906560 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3×C5 |
| abelian | C22×C3×C52×C8×C9 |
| multiplicative | (ℤ/24149)ˣ, (ℤ/24893)ˣ, (ℤ/34317)ˣ, (ℤ/48298)ˣ, (ℤ/49786)ˣ, (ℤ/68634)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C23×C32×C52 |
| socle, prime radical | C23×C32×C52 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3040 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C31×C41 |
| outer automorphism group of | C19×C31×C41 |
Past the SmallGroups library coverage — no SmallGroups id.