Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×D3×#543 |
| Fitting | C2×C3×#543 ⋊ C2 |
| Sylow | C3 ⋊ C22×#543 |
9310 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3490, D3×#11394, C2×D3×#2032, … |
| maximal normal subgroup of | C2×D3×#3490, D3×#11394, C2×D3×#2032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076288);