Finite Group DatabasebetaFinite Group Databasebeta| order | 28160 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 31457280 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C5×C11×C32 |
| multiplicative | (ℤ/58245)ˣ, (ℤ/62128)ˣ, (ℤ/70600)ˣ, (ℤ/73600)ˣ, (ℤ/77440)ˣ, (ℤ/77660)ˣ, (ℤ/105900)ˣ, (ℤ/116490)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C16 | C24×C5×C11 |
| socle, prime radical | C24×C5×C11 | C2×C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2568 conjugacy classes of subgroups.
28160 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.