Finite Group DatabasebetaFinite Group Databasebeta| order | 24024 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 241920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C7×C11×C13 |
| multiplicative | (ℤ/37743)ˣ, (ℤ/42063)ˣ, (ℤ/48056)ˣ, (ℤ/50324)ˣ, (ℤ/56084)ˣ, (ℤ/72084)ˣ, (ℤ/72108)ˣ, (ℤ/75486)ˣ, (ℤ/84126)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
24024 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.