Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#14558804 |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C9 |
| derived | C7×C19 ⋊ C2×C7×C9 |
| Hall | C7×#11924781 ⋊ C2 |
| Hall | C7×D7×C19 ⋊ C9 |
| Hall | C7×D7 ⋊ #4296 |
| Sylow | C72 ⋊ C2×#4296 |
| Sylow | C19 ⋊ C7×D7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #14558804 |
| commutator, hypocenter | C7×C19 | C2×C7×C9 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C9 |
| prime radical | C7×D7×C19⋊C3 | C3 |
| cosocle | C7×C19⋊C3 | C2×C3×C7 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 798 |
217 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14558802⋊C2, #14558804⋊D7, D7×#14558804, … |
| maximal normal subgroup of | C7×#14558802⋊C2, #14558804⋊D7, D7×#14558804, … |
| maximal quotient of | C7×#18012154, C2×C7×#14558804 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 166);