Finite Group DatabasebetaFinite Group Databasebeta| order | 7872 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 825753600 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C3×C4×C41 |
| multiplicative | (ℤ/23240)ˣ, (ℤ/25896)ˣ, (ℤ/27888)ˣ, (ℤ/29880)ˣ, (ℤ/34860)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C25×C3×C41 |
| socle, prime radical | C25×C3×C41 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2724 conjugacy classes of subgroups.
7872 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.