Finite Group DatabasebetaFinite Group Databasebeta| order | 21600 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 115935805440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C33×C5 |
| abelian | C23×C33×C4×C52 |
| multiplicative | (ℤ/31031)ˣ, (ℤ/39711)ˣ, (ℤ/39897)ˣ, (ℤ/42273)ˣ, (ℤ/48825)ˣ, (ℤ/52948)ˣ, (ℤ/62062)ˣ, (ℤ/68076)ˣ, (ℤ/79422)ˣ, (ℤ/79794)ˣ, (ℤ/84546)ˣ, (ℤ/97650)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C33×C52 |
| socle, prime radical | C24×C33×C52 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
26432 conjugacy classes of subgroups.
21600 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.