Finite Group DatabasebetaFinite Group Databasebeta| order | 7040 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3440640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C5×C11×C16 |
| multiplicative | (ℤ/12903)ˣ, (ℤ/16192)ˣ, (ℤ/16456)ˣ, (ℤ/17204)ˣ, (ℤ/21144)ˣ, (ℤ/23232)ˣ, (ℤ/24684)ˣ, (ℤ/25806)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C24×C5×C11 |
| socle, prime radical | C24×C5×C11 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
880 conjugacy classes of subgroups.
7040 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.