Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊D19 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)×D19) |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C32 |
| Hall | C19×ΓL(1,𝔽8)2 ⋊ C2 |
| Hall | C7×D133 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ D19 |
| Sylow | C72 ⋊ C32×D19 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C19 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
100 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 798 |
260 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 213);