Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×#1313 |
| Fitting | C3×#1313 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1313 |
302 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12067, C3⋊D3×#1313, D3×#7333, … |
| maximal normal subgroup of | D3×#12067, D3×#7333, D3×#12068, … |
| maximal quotient of | C3⋊D3×#1313, D3×#7333, #72222588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 78563);