Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | S4×#104 |
| Fitting | C22×#104 ⋊ D3 |
846 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #104×#857, S4×#857, #72226072, … |
| maximal normal subgroup of | S4×#444, S4×#453, S4×#421, … |
| maximal quotient of | #104×#857, #72226072, S4×D4⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087299);