Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C22⋊C4×C42⋊C3 |
| unambiguous semidirect product | (C42×C22⋊C4)⋊C3 |
| Fitting, Sylow | C42×C22⋊C4 ⋊ C3 |
642 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #72225966, C22⋊C4×#857, #72226107, … |
| maximal normal subgroup of | #72225966, C22⋊C4×#857, #72226107, … |
| maximal quotient of | #104×C42⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083582);