Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
| direct product | S4×C22⋊C8 |
| Fitting | C22×C22⋊C8 ⋊ D3 |
1046 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 1046 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D4×S4, S4×#450, #72343905, … |
| maximal normal subgroup of | C8×D4×S4, S4×#450, S4×#447 |
| maximal quotient of | S4×D4⋊C8, S4×#350 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087268);