Finite Group DatabasebetaFinite Group Databasebeta| order | 770 |
| isoclinism | isoclinic class of D35 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D35 |
| unambiguous semidirect product | C5⋊(C11×D7) |
| unambiguous semidirect product | C7⋊(D5×C11) |
| Fitting, socle, Hall | C5×C7×C11 ⋊ C2 |
| derived, Hall | C5×C7 ⋊ C2×C11 |
| Hall | C7×C11 ⋊ D5 |
| Hall | C5×C11 ⋊ D7 |
| Sylow | C7 ⋊ D5×C11 |
| Sylow | C5 ⋊ C11×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D35 |
| commutator, cosocle, hypocenter | C5×C7 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11 | C2 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 385 |
209 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D35, D5×C11×D7, D35⋊D11, … |
| maximal normal subgroup of | D11×D35, D5×C11×D7, D35⋊D11, … |
| maximal quotient of | C11×Dic35, C2×C11×D35, C3×C11×D35, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(770, 10);