Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D3×#2132 |
| Fitting | C3×#2132 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2132 |
1306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#12718, D3×#33570, D3×#12765, … |
| maximal normal subgroup of | D3×#12718, D3×#33570, D3×#12765, … |
| maximal quotient of | D3×#12585 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322394);