Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | D4×A4⋊C8 |
750 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 109 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 | C8×D4×S4, #72342692, #72342710 |
| maximal normal subgroup of | C8×D4×S4, #72342692, #72342710 |
| maximal quotient of | #72342710, #72342873 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087269);