Finite Group DatabasebetaFinite Group Databasebeta| order | 24000 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 12800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C32×C125 |
| multiplicative | (ℤ/24347)ˣ, (ℤ/28007)ˣ, (ℤ/36009)ˣ, (ℤ/48694)ˣ, (ℤ/56014)ˣ, (ℤ/72018)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16×C25 | C22×C3×C5 |
| socle, prime radical | C22×C3×C5 | C16×C25 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
136 conjugacy classes of subgroups.
24000 conjugacy classes. The character table is too large to display.
| automorphism group of | C97×C251 |
| outer automorphism group of | C97×C251 |
Past the SmallGroups library coverage — no SmallGroups id.