Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C72×C19 ⋊ C2×C32 |
| derived | C7×C19 ⋊ C2×C32×C7 |
| Hall | C7×ΓL(1,𝔽8)×C19⋊C3 ⋊ C2 |
| Hall | C7×D7×C19 ⋊ C32 |
| Hall | C7×D7 ⋊ C3×C19⋊C3 |
| Sylow | C72 ⋊ C2×C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | AGL(1,𝔽7)×C19⋊C3 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C19 | C2×C32 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C7 | |
100 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 798 |
441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 168);