Finite Group DatabasebetaFinite Group Databasebeta| order | 8640 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 331776 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C22×C3×C5×C9×C16 |
| multiplicative | (ℤ/10013)ˣ, (ℤ/13737)ˣ, (ℤ/14229)ˣ, (ℤ/18316)ˣ, (ℤ/20026)ˣ, (ℤ/26028)ˣ, (ℤ/27474)ˣ, (ℤ/28458)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C8 | C23×C32×C5 |
| socle, prime radical | C23×C32×C5 | C3×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
980 conjugacy classes of subgroups.
8640 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.