Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×S4)⋊C8 |
| Fitting | C24×C8 ⋊ D3 |
1117 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1117 conjugacy classes of subgroups — too many to draw. Only its 117 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 | C2×C8×GL(2,ℤ/4) |
| maximal normal subgroup of | C2×C8×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087085);