Finite Group DatabasebetaFinite Group Databasebeta| order | 8480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4472832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C5×C53 |
| multiplicative | (ℤ/17655)ˣ, (ℤ/18832)ˣ, (ℤ/21400)ˣ, (ℤ/23540)ˣ, (ℤ/25464)ˣ, (ℤ/32100)ˣ, (ℤ/35310)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C5×C53 |
| socle, prime radical | C24×C5×C53 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
472 conjugacy classes of subgroups.
8480 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.