Finite Group DatabasebetaFinite Group Databasebeta| order | 22176 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7741440 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C7×C9×C11 |
| multiplicative | (ℤ/38019)ˣ, (ℤ/43815)ˣ, (ℤ/46168)ˣ, (ℤ/46736)ˣ, (ℤ/50692)ˣ, (ℤ/58420)ˣ, (ℤ/69252)ˣ, (ℤ/72036)ˣ, (ℤ/76038)ˣ, (ℤ/87630)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C24×C3×C7×C11 |
| socle, prime radical | C24×C3×C7×C11 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1416 conjugacy classes of subgroups.
22176 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.