Finite Group DatabasebetaFinite Group Databasebeta| order | 7742 |
| isoclinism | isoclinic class of D79 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D79 |
| unambiguous semidirect product | C79⋊(C2×C49) |
| Fitting, Hall | C49×C79 ⋊ C2 |
| derived, Sylow | C79 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D79 |
| commutator, hypocenter | C79 | C2×C49 |
| Frattini | C7 | C7×D79 |
| Fitting | C49×C79 | C2 |
| socle | C7×C79 | C2×C7 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C49 | |
12 conjugacy classes of subgroups.
2009 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D49×D79, C2×C49×D79, C3×C49×D79, … |
| maximal normal subgroup of | D49×D79, C2×C49×D79, C3×C49×D79, … |
| maximal quotient of | C49×Dic79, C2×C49×D79, C3×C49×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7742, 3);