Finite Group DatabasebetaFinite Group Databasebeta| order | 24480 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 8257536 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C5×C9×C17 |
| multiplicative | (ℤ/50655)ˣ, (ℤ/53944)ˣ, (ℤ/54032)ˣ, (ℤ/61240)ˣ, (ℤ/61400)ˣ, (ℤ/67540)ˣ, (ℤ/73464)ˣ, (ℤ/73488)ˣ, (ℤ/80916)ˣ, (ℤ/91860)ˣ, (ℤ/92100)ˣ, (ℤ/101310)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C24×C3×C5×C17 |
| socle, prime radical | C24×C3×C5×C17 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
24480 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.