Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | D3×#1910 |
| Fitting | C3×#1910 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1910 |
1878 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | #72214537, D3×#23882, D3×#12778, … |
| maximal normal subgroup of | D3×#23882, D3×#12778, D3×#12755, … |
| maximal quotient of | #72214537, C2×D3×#1910, D3×#10742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171543);