Finite Group DatabasebetaFinite Group Databasebeta| order | 7660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic383 |
| unambiguous semidirect product | C383⋊(C4×C5) |
| derived, Sylow | C383 ⋊ C4×C5 |
| Hall | C5×C383 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D383 |
| commutator, hypocenter | C383 | C4×C5 |
| Frattini | C2 | C5×D383 |
| Fitting, socle | C2×C5×C383 | C2 |
| LCS | G ▷ C383 | |
| UCS | C1 ◁ C2×C5 | |
12 conjugacy classes of subgroups.
1930 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic383, C5×Dic1149, C25×Dic383, … |
| maximal normal subgroup of | C3×C5×Dic383, C25×Dic383, C52×Dic383 |
| maximal quotient of | C3×C5×Dic383, C5×Dic1149, C25×Dic383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7660, 3);