Finite Group DatabasebetaFinite Group Databasebeta| order | 28266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D673⋊C3 |
| Fitting, socle, Hall | C7×C673 ⋊ C2×C3 |
| derived, Sylow | C673 ⋊ C2×C3×C7 |
| Hall | C7×C673⋊C3 ⋊ C2 |
| Hall | C7×D673 ⋊ C3 |
| Hall | C673⋊C3 ⋊ C2×C7 |
| Hall | D673 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D673⋊C3 |
| commutator, cosocle, hypocenter | C673 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C673 | C2×C3 |
| LCS | G ▷ C673 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4711 |
826 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28266, 18);