Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×GL(2,ℤ/4)⋊C4 |
| Fitting | C23×C22⋊C4 ⋊ D3 |
2669 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 2669 conjugacy classes of subgroups — too many to draw. Only its 213 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 | C2×#11923458, C2×#11714540, D3×GL(2,ℤ/4)⋊C4, … |
| maximal normal subgroup of | C2×#11714540, #72259035, #72259036, … |
| maximal quotient of | #72226110, #72226188, #72226192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088684);