Finite Group DatabasebetaFinite Group Databasebeta| order | 742 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | D7×C53 |
| unambiguous semidirect product | C7⋊(C2×C53) |
| Fitting, socle, Hall | C7×C53 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C7×C53 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C53 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 371 |
265 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D53, C2×D7×C53, C3×D7×C53, … |
| maximal normal subgroup of | D7×D53, C2×D7×C53, C3×D7×C53, … |
| maximal quotient of | Dic7×C53, C2×D7×C53, C3×D7×C53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(742, 1);