Finite Group DatabasebetaFinite Group Databasebeta| order | 23760 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 69120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C2×C3×C5×C8×C9×C11 |
| multiplicative | (ℤ/24163)ˣ, (ℤ/25099)ˣ, (ℤ/35667)ˣ, (ℤ/48326)ˣ, (ℤ/50198)ˣ, (ℤ/71334)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C22×C32×C5×C11 |
| socle, prime radical | C22×C32×C5×C11 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
440 conjugacy classes of subgroups.
23760 conjugacy classes. The character table is too large to display.
| automorphism group of | C73×C331, C19×C1321 |
| outer automorphism group of | C73×C331, C19×C1321 |
Past the SmallGroups library coverage — no SmallGroups id.