Finite Group DatabasebetaFinite Group Databasebeta| order | 24480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 147456 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C5×C8×C9×C17 |
| multiplicative | (ℤ/28633)ˣ, (ℤ/37761)ˣ, (ℤ/40689)ˣ, (ℤ/48968)ˣ, (ℤ/48992)ˣ, (ℤ/50348)ˣ, (ℤ/57266)ˣ, (ℤ/73452)ˣ, (ℤ/75522)ˣ, (ℤ/81378)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C23×C3×C5×C17 |
| socle, prime radical | C23×C3×C5×C17 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
456 conjugacy classes of subgroups.
24480 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.