Finite Group DatabasebetaFinite Group Databasebeta| order | 23328 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 30474952704 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C32×C9 |
| abelian | C23×C3×C4×C9×C27 |
| multiplicative | (ℤ/43491)ˣ, (ℤ/53865)ˣ, (ℤ/57988)ˣ, (ℤ/74556)ˣ, (ℤ/80028)ˣ, (ℤ/82404)ˣ, (ℤ/83916)ˣ, (ℤ/86982)ˣ, (ℤ/107730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3×C9 | C24×C33 |
| socle, prime radical | C24×C33 | C2×C3×C9 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
23836 conjugacy classes of subgroups.
23328 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.