Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
| direct product | C2×#87508 |
1557 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 1557 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #72227567, C2×#11715706, C2×#72212847 |
| maximal normal subgroup of | #72227567, C2×#11715706 |
| maximal quotient of | #72227567, C2×#72212847, C2×#11715653, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1090196);