Finite Group DatabasebetaFinite Group Databasebeta| order | 10766 |
| automorphism | Aut(G) order 24804864 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5383 |
| unambiguous semidirect product | C7⋊D769 |
| unambiguous semidirect product | C769⋊D7 |
| Fitting, socle, derived, Hall | C7×C769 ⋊ C2 |
| Sylow | C769 ⋊ D7 |
| Sylow | C7 ⋊ D769 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C769 | C2 |
| LCS | G ▷ C7×C769 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,769|b^a=b^6,c^a=c^7682693 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D769, C2×D5383, C3×D5383, … |
| maximal normal subgroup of | D7×D769, C2×D5383, C3×D5383, … |
| maximal quotient of | Dic5383, C2×D5383, C3×D5383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10766, 3);