Finite Group DatabasebetaFinite Group Databasebeta| order | 7670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D767 |
| unambiguous semidirect product | C13⋊(C5×D59) |
| unambiguous semidirect product | C59⋊(C5×D13) |
| Fitting, socle, Hall | C5×C13×C59 ⋊ C2 |
| derived, Hall | C13×C59 ⋊ C2×C5 |
| Hall | C5×C59 ⋊ D13 |
| Hall | C5×C13 ⋊ D59 |
| Sylow | C59 ⋊ C5×D13 |
| Sylow | C13 ⋊ C5×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D767 |
| commutator, hypocenter | C13×C59 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C59 | C2 |
| LCS | G ▷ C13×C59 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
1925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D13×D59, D5×D767, D65⋊D59, … |
| maximal normal subgroup of | C5×D13×D59, D5×D767, D65⋊D59, … |
| maximal quotient of | C5×Dic767, C2×C5×D767, C3×C5×D767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7670, 4);