Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#5409 |
2225 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 2225 conjugacy classes of subgroups — too many to draw. Only its 285 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×#5409, #72226192, C22×#85489, … |
| maximal normal subgroup of | A4×#5409, #72226192, C22×#85489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1088977);