Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D8×SL(2,ℤ/4) |
745 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 745 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | D8×GL(2,ℤ/4), AGL(1,ℤ/8)×SL(2,ℤ/4), #72258881, … |
| maximal normal subgroup of | D8×GL(2,ℤ/4), AGL(1,ℤ/8)×SL(2,ℤ/4), #72258881, … |
| maximal quotient of | #72342730, #72342785 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087315);