Finite Group DatabasebetaFinite Group Databasebeta| order | 770 |
| isoclinism | isoclinic class of D77 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D77 |
| unambiguous semidirect product | C7⋊(C5×D11) |
| Fitting, socle, Hall | C5×C7×C11 ⋊ C2 |
| derived, Hall | C7×C11 ⋊ C2×C5 |
| Hall | C5×C11 ⋊ D7 |
| Hall | C5×C7 ⋊ D11 |
| Sylow | C11 ⋊ C5×D7 |
| Sylow | C7 ⋊ C5×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D77 |
| commutator, cosocle, hypocenter | C7×C11 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11 | C2 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 385 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D7×D11, D5×D77, D35⋊D11, … |
| maximal normal subgroup of | C5×D7×D11, D5×D77, D35⋊D11, … |
| maximal quotient of | C5×Dic77, C2×C5×D77, C3×C5×D77, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(770, 7);