Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 153600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C16×C125 |
| multiplicative | (ℤ/29869)ˣ, (ℤ/38301)ˣ, (ℤ/38403)ˣ, (ℤ/48064)ˣ, (ℤ/51068)ˣ, (ℤ/59738)ˣ, (ℤ/76602)ˣ, (ℤ/76806)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8×C25 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C8×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
392 conjugacy classes of subgroups.
24000 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.