Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#72989 |
916 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 916 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11713151, C2×#1020⋊Q8, C2×#11713216, … |
| maximal normal subgroup of | C2×#11713151, C2×#1020⋊Q8, C2×#11713216, … |
| maximal quotient of | C2×#11711653 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1087528);