Finite Group DatabasebetaFinite Group Databasebeta| order | 22132 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic503 |
| unambiguous semidirect product | C503⋊(C4×C11) |
| derived, Sylow | C503 ⋊ C4×C11 |
| Hall | C11×C503 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D503 |
| commutator, hypocenter | C503 | C4×C11 |
| Frattini | C2 | C11×D503 |
| Fitting, socle, prime radical | C2×C11×C503 | C2 |
| cosocle | C2×C503 | C2×C11 |
| LCS | G ▷ C503 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22132 |
5566 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22132, 3);