Finite Group DatabasebetaFinite Group Databasebeta| order | 23688 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2225664 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C3 |
| abelian | C23×C32×C7×C47 |
| multiplicative | (ℤ/36507)ˣ, (ℤ/41517)ˣ, (ℤ/41601)ˣ, (ℤ/48676)ˣ, (ℤ/55468)ˣ, (ℤ/73014)ˣ, (ℤ/83034)ˣ, (ℤ/83202)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
384 conjugacy classes of subgroups.
23688 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.