Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 29491200 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C3×C42×C125 |
| multiplicative | (ℤ/48945)ˣ, (ℤ/52208)ˣ, (ℤ/60080)ˣ, (ℤ/65000)ˣ, (ℤ/65260)ˣ, (ℤ/70000)ˣ, (ℤ/90000)ˣ, (ℤ/97500)ˣ, (ℤ/97890)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C25 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C22×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1992 conjugacy classes of subgroups.
24000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.