Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | S4×#97 |
| Fitting | C22×#97 ⋊ D3 |
683 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 683 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #72227323, S4×#442, S4×#347, … |
| maximal normal subgroup of | S4×#442, S4×#347, S4×#444 |
| maximal quotient of | S4×#347, #97×GL(2,𝔽3), #97×C3⋊S4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1086954);