Finite Group DatabasebetaFinite Group Databasebeta| order | 23616 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 10321920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C8×C9×C41 |
| multiplicative | (ℤ/48472)ˣ, (ℤ/50464)ˣ, (ℤ/70872)ˣ, (ℤ/70944)ˣ, (ℤ/71712)ˣ, (ℤ/72708)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C4 | C24×C3×C41 |
| socle, prime radical | C24×C3×C41 | C3×C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1014 conjugacy classes of subgroups.
23616 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.