Finite Group DatabasebetaFinite Group Databasebeta| order | 19008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 46448640 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C23×C3×C8×C9×C11 |
| multiplicative | (ℤ/35259)ˣ, (ℤ/35511)ˣ, (ℤ/39128)ˣ, (ℤ/40736)ˣ, (ℤ/44576)ˣ, (ℤ/47012)ˣ, (ℤ/47348)ˣ, (ℤ/57312)ˣ, (ℤ/57888)ˣ, (ℤ/58692)ˣ, (ℤ/60444)ˣ, (ℤ/60876)ˣ, (ℤ/67284)ˣ, (ℤ/70518)ˣ, (ℤ/71022)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C24×C32×C11 |
| socle, prime radical | C24×C32×C11 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3380 conjugacy classes of subgroups.
19008 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.