Finite Group DatabasebetaFinite Group Databasebeta| order | 7742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D553 |
| unambiguous semidirect product | C79⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C79 ⋊ C2 |
| Sylow | C79 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C79 | C2 |
| LCS | G ▷ C72×C79 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,7^2,79|b^a=b^6,c^a=c^6,d^a=d^781937 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7⋊D7×D79, D7×D553, C2×C7⋊D553, … |
| maximal normal subgroup of | C7⋊D7×D79, D7×D553, C2×C7⋊D553, … |
| maximal quotient of | C7⋊Dic553, C2×C7⋊D553, C3×C7⋊D553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7742, 10);