Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2064384000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C3×C4×C125 |
| multiplicative | (ℤ/70280)ˣ, (ℤ/78312)ˣ, (ℤ/84336)ˣ, (ℤ/90120)ˣ, (ℤ/90360)ˣ, (ℤ/105000)ˣ, (ℤ/105420)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C25 | C25×C3×C5 |
| socle, prime radical | C25×C3×C5 | C2×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
5448 conjugacy classes of subgroups.
24000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.