Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 30720 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C3×C16×C25 |
| multiplicative | (ℤ/7701)ˣ, (ℤ/8421)ˣ, (ℤ/9608)ˣ, (ℤ/9664)ˣ, (ℤ/10268)ˣ, (ℤ/11228)ˣ, (ℤ/14412)ˣ, (ℤ/14436)ˣ, (ℤ/15402)ˣ, (ℤ/16842)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C5×C8 | C23×C3×C5 |
| socle, prime radical | C23×C3×C5 | C5×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
294 conjugacy classes of subgroups.
4800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.