Finite Group DatabasebetaFinite Group Databasebeta| order | 24360 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 225792 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C5×C7×C29 |
| multiplicative | (ℤ/27907)ˣ, (ℤ/29323)ˣ, (ℤ/31801)ˣ, (ℤ/37347)ˣ, (ℤ/37701)ˣ, (ℤ/48728)ˣ, (ℤ/49796)ˣ, (ℤ/55814)ˣ, (ℤ/58646)ˣ, (ℤ/63602)ˣ, (ℤ/73092)ˣ, (ℤ/74694)ˣ, (ℤ/75402)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
24360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.