Finite Group DatabasebetaFinite Group Databasebeta| order | 16758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×ΓL(1,𝔽8)×#87705 |
| Fitting, socle, Hall | C2×C72×C19 ⋊ C32 |
| derived, Hall | C72×C19 ⋊ C2×C32 |
| Hall | C2×C72 ⋊ C3×C19⋊C3 |
| Sylow | C72 ⋊ C2×C3×C19⋊C3 |
| Hall | C2×C19 ⋊ ΓL(1,𝔽8)2 |
| Sylow | C19 ⋊ C2×ΓL(1,𝔽8)2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)×#87705 |
| commutator, cosocle, hypocenter | C72×C19 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
112 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 798 |
470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16758, 270);