Finite Group DatabasebetaFinite Group Databasebeta| order | 24320 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 221184 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C5×C19×C64 |
| multiplicative | (ℤ/40161)ˣ, (ℤ/48896)ˣ, (ℤ/53548)ˣ, (ℤ/80322)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C23×C5×C19 |
| socle, prime radical | C23×C5×C19 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
284 conjugacy classes of subgroups.
24320 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.