Finite Group DatabasebetaFinite Group Databasebeta| order | 22092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D789 |
| unambiguous semidirect product | (C2×C3)⋊(C7×D263) |
| unambiguous semidirect product | (C2×C263)⋊(D3×C7) |
| Fitting, socle | C2×C3×C7×C263 ⋊ C2 |
| derived, Hall | C3×C263 ⋊ C22×C7 |
| Hall | C3×C7×C263 ⋊ C22 |
| Hall | C7×C263 ⋊ C2×D3 |
| Sylow | C263 ⋊ C2×D3×C7 |
| Hall | C3×C7 ⋊ C2×D263 |
| Sylow | C3 ⋊ C2×C7×D263 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D789 |
| commutator, cosocle, hypocenter | C3×C263 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C263 | C2 |
| LCS | G ▷ C3×C263 | |
| UCS | C1 ◁ C2×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11046 |
5544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22092, 32);