Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | A4×D4⋊C8 |
| unambiguous semidirect product | D4⋊(C8×A4) |
| unambiguous semidirect product | (C22×D4⋊C8)⋊C3 |
| Fitting, Sylow | C22×D4⋊C8 ⋊ C3 |
451 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#1580, S4×D4⋊C8, #72342692 |
| maximal normal subgroup of | A4×#1580, S4×D4⋊C8, #72342692 |
| maximal quotient of | A4×#1333, A4×#1336 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083743);