Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D3×#1914 |
| Fitting | C3×#1914 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1914 |
1862 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | #72214374, D3×#23872, D3×#12755, … |
| maximal normal subgroup of | D3×#23872, D3×#12755, D3×#12756, … |
| maximal quotient of | #72214374, C2×D3×#1914, D3×#10755 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171587);