Finite Group DatabasebetaFinite Group Databasebeta| order | 22396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C509 · Schur multiplier (H2) = C1 |
| direct product | Dic11×C509 |
| unambiguous semidirect product | C11⋊(C4×C509) |
| derived, Sylow | C11 ⋊ C4×C509 |
| Hall | C11×C509 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C509 | D11 |
| commutator, hypocenter | C11 | C4×C509 |
| Frattini | C2 | D11×C509 |
| Fitting, socle, prime radical | C2×C11×C509 | C2 |
| cosocle | C2×C11 | C2×C509 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C509 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 22396 |
7126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22396, 2);