Finite Group DatabasebetaFinite Group Databasebeta| order | 7680 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 25165824 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C8 |
| abelian | C22×C3×C5×C8×C16 |
| multiplicative | (ℤ/14637)ˣ, (ℤ/16864)ˣ, (ℤ/18368)ˣ, (ℤ/19516)ˣ, (ℤ/23136)ˣ, (ℤ/23616)ˣ, (ℤ/25092)ˣ, (ℤ/29274)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C4×C8 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C4×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3848 conjugacy classes of subgroups.
7680 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.