Finite Group DatabasebetaFinite Group Databasebeta| order | 24960 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8257536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C5×C13×C16 |
| multiplicative | (ℤ/44319)ˣ, (ℤ/46767)ˣ, (ℤ/55616)ˣ, (ℤ/58688)ˣ, (ℤ/59092)ˣ, (ℤ/62356)ˣ, (ℤ/74904)ˣ, (ℤ/75456)ˣ, (ℤ/80172)ˣ, (ℤ/88638)ˣ, (ℤ/93534)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C24×C3×C5×C13 |
| socle, prime radical | C24×C3×C5×C13 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1760 conjugacy classes of subgroups.
24960 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.