Finite Group DatabasebetaFinite Group Databasebeta| order | 24840 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1596672 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C3×C5×C9×C23 |
| multiplicative | (ℤ/27683)ˣ, (ℤ/29051)ˣ, (ℤ/39339)ˣ, (ℤ/39387)ˣ, (ℤ/41283)ˣ, (ℤ/52516)ˣ, (ℤ/55366)ˣ, (ℤ/58102)ˣ, (ℤ/74628)ˣ, (ℤ/78678)ˣ, (ℤ/78774)ˣ, (ℤ/82566)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C32×C5×C23 |
| socle, prime radical | C23×C32×C5×C23 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
640 conjugacy classes of subgroups.
24840 conjugacy classes. The character table is too large to display.
| automorphism group of | C19×C31×C47 |
| outer automorphism group of | C19×C31×C47 |
Past the SmallGroups library coverage — no SmallGroups id.