Finite Group DatabasebetaFinite Group Databasebeta| order | 23688 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 278208 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C7×C9×C47 |
| multiplicative | (ℤ/37563)ˣ, (ℤ/47384)ˣ, (ℤ/50084)ˣ, (ℤ/71076)ˣ, (ℤ/71172)ˣ, (ℤ/75126)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3 | C23×C3×C7×C47 |
| socle, prime radical | C23×C3×C7×C47 | C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
192 conjugacy classes of subgroups.
23688 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.