Finite Group DatabasebetaFinite Group Databasebeta| order | 22464 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 55738368 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C8×C9×C13 |
| multiplicative | (ℤ/46136)ˣ, (ℤ/47576)ˣ, (ℤ/48032)ˣ, (ℤ/52472)ˣ, (ℤ/67464)ˣ, (ℤ/67608)ˣ, (ℤ/68256)ˣ, (ℤ/69204)ˣ, (ℤ/71364)ˣ, (ℤ/78708)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C24×C32×C13 |
| socle, prime radical | C24×C32×C13 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3380 conjugacy classes of subgroups.
22464 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.