Finite Group DatabasebetaFinite Group Databasebeta| order | 6560 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3440640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C5×C41 |
| multiplicative | (ℤ/13695)ˣ, (ℤ/14608)ˣ, (ℤ/16600)ˣ, (ℤ/18260)ˣ, (ℤ/19704)ˣ, (ℤ/24900)ˣ, (ℤ/27390)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C5×C41 |
| socle, prime radical | C24×C5×C41 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
472 conjugacy classes of subgroups.
6560 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.