Finite Group DatabasebetaFinite Group Databasebeta| order | 18944 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 452984832 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C43 |
| abelian | C2×C42×C16×C37 |
| multiplicative | (ℤ/37995)ˣ, (ℤ/40528)ˣ, (ℤ/47440)ˣ, (ℤ/47680)ˣ, (ℤ/50660)ˣ, (ℤ/75990)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22×C8 | C24×C37 |
| socle, prime radical | C24×C37 | C22×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2820 conjugacy classes of subgroups.
18944 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.