Finite Group DatabasebetaFinite Group Databasebeta| order | 16786 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C109 · Schur multiplier (H2) = C1 |
| direct product | C11×D7×C109 |
| unambiguous semidirect product | C7⋊(C2×C11×C109) |
| Fitting, socle, Hall | C7×C11×C109 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C11×C109 |
| Hall | C7×C109 ⋊ C2×C11 |
| Hall | C7×C11 ⋊ C2×C109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C109 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C11×C109 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C109 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C11×C109 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8393 |
5995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D7×D109, D7×D11×C109, D7×D1199, … |
| maximal normal subgroup of | C11×D7×D109, D7×D11×C109, D7×D1199, … |
| maximal quotient of | C11×Dic7×C109, C2×C11×D7×C109 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16786, 5);