Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3072000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C5 |
| abelian | C22×C3×C5×C16×C25 |
| multiplicative | (ℤ/28237)ˣ, (ℤ/30877)ˣ, (ℤ/37293)ˣ, (ℤ/39633)ˣ, (ℤ/39699)ˣ, (ℤ/49724)ˣ, (ℤ/52844)ˣ, (ℤ/56474)ˣ, (ℤ/61754)ˣ, (ℤ/74586)ˣ, (ℤ/79266)ˣ, (ℤ/79398)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C8 | C23×C3×C52 |
| socle, prime radical | C23×C3×C52 | C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1372 conjugacy classes of subgroups.
24000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.