Finite Group DatabasebetaFinite Group Databasebeta| order | 7690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D769 |
| unambiguous semidirect product | C769⋊(C2×C5) |
| Fitting, socle, Hall | C5×C769 ⋊ C2 |
| derived, Sylow | C769 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D769 |
| commutator, hypocenter | C769 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C769 | C2 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
1930 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#15690484, #29506980, D5×D769, … |
| maximal normal subgroup of | C5×#15690484, #29506980, D5×D769, … |
| maximal quotient of | C5×Dic769, C2×C5×D769, C3×C5×D769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7690, 2);