Finite Group DatabasebetaFinite Group Databasebeta| order | 4800 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1966080 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C4×C5 |
| abelian | C2×C3×C4×C52×C8 |
| multiplicative | (ℤ/5863)ˣ, (ℤ/6355)ˣ, (ℤ/7175)ˣ, (ℤ/7503)ˣ, (ℤ/9225)ˣ, (ℤ/10004)ˣ, (ℤ/11726)ˣ, (ℤ/12710)ˣ, (ℤ/14350)ˣ, (ℤ/15006)ˣ, (ℤ/18450)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C4 | C23×C3×C52 |
| socle, prime radical | C23×C3×C52 | C2×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1296 conjugacy classes of subgroups.
4800 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.