Finite Group DatabasebetaFinite Group Databasebeta| order | 3520 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 412876800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C4×C5×C11 |
| multiplicative | (ℤ/10120)ˣ, (ℤ/12144)ˣ, (ℤ/13800)ˣ, (ℤ/14520)ˣ, (ℤ/15180)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C5×C11 |
| socle, prime radical | C25×C5×C11 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2724 conjugacy classes of subgroups.
3520 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.