Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×#834 |
| Sylow | C3 ⋊ D4×#99 |
2102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D4×#99, D4×#5244, D4×#5032, … |
| maximal normal subgroup of | D3×D4×#99, D4×#5244, D4×#5032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 184892);