Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C8 |
| direct product | C2×#71276 |
| Fitting | C2×C3×#493 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1712 |
1342 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 283 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1712, #72225919, #72226002, … |
| maximal normal subgroup of | C2×D3×#1712, #72225919, #72226002, … |
| maximal quotient of | #72225918, #72225919, #72225930 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 157258);