Finite Group DatabasebetaFinite Group Databasebeta| order | 7678 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C349 · Schur multiplier (H2) = C1 |
| direct product | D11×C349 |
| unambiguous semidirect product | C11⋊(C2×C349) |
| Fitting, socle, Hall | C11×C349 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C349 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C349 | D11 |
| commutator, hypocenter | C11 | C2×C349 |
| Frattini | C1 | G |
| Fitting, socle | C11×C349 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C349 | |
8 conjugacy classes of subgroups.
2443 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D349, C2×D11×C349, C3×D11×C349, … |
| maximal normal subgroup of | D11×D349, C2×D11×C349, C3×D11×C349, … |
| maximal quotient of | Dic11×C349, C2×D11×C349, C3×D11×C349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7678, 1);