Finite Group DatabasebetaFinite Group Databasebeta| order | 15785 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#14555917 |
| Fitting, socle, Hall | C7×C11×C41 ⋊ C5 |
| derived, Hall | C11×C41 ⋊ C5×C7 |
| Hall | C7×C41 ⋊ C11⋊C5 |
| Hall | C7×C11 ⋊ C41⋊C5 |
| Sylow | C41 ⋊ C7×C11⋊C5 |
| Sylow | C11 ⋊ C7×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #14555917 |
| commutator, cosocle, hypocenter | C11×C41 | C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C41 | C5 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3157 |
665 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×#14555917, C7×#17985236, C7×#17985242, … |
| maximal normal subgroup of | C2×C7×#14555917, C7×#17985236, C7×#17985242, … |
| maximal quotient of | C2×C7×#14555917 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15785, 5);