Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#69339 |
| Fitting | C2×C3×#367 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2177 |
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2177, C2×#11797807, C2×#10715811, … |
| maximal normal subgroup of | C2×D3×#2177, C2×#10715811, C2×#10715809 |
| maximal quotient of | C2×#11797807, C2×#10715811 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322870);