Finite Group DatabasebetaFinite Group Databasebeta| order | 24024 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 11520 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C3×C4×C7×C11×C13 |
| multiplicative | (ℤ/24539)ˣ, (ℤ/24911)ˣ, (ℤ/25139)ˣ, (ℤ/26039)ˣ, (ℤ/30035)ˣ, (ℤ/49078)ˣ, (ℤ/49822)ˣ, (ℤ/50278)ˣ, (ℤ/52078)ˣ, (ℤ/60070)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C22×C3×C7×C11×C13 |
| socle, prime radical | C22×C3×C7×C11×C13 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
128 conjugacy classes of subgroups.
24024 conjugacy classes. The character table is too large to display.
| automorphism group of | C53×C463, C29×C859, C23×C1093 |
| outer automorphism group of | C53×C463, C29×C859, C23×C1093 |
Past the SmallGroups library coverage — no SmallGroups id.