Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#68721 |
| Fitting | C2×C3×#338 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2091 |
1102 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10909605, C2×D3×#2091, #72248382, … |
| maximal normal subgroup of | C2×#10909605, C2×D3×#2091, #72248382, … |
| maximal quotient of | #72269949 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 199316);