Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×C4×D3×C22⋊C4 |
| Fitting | C2×C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C22×C4×C22⋊C4 |
9534 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D3×#120, C2×D3×D4×C22⋊C4, C2×D3×#2433, … |
| maximal normal subgroup of | C2×C4×D3×#120, C2×D3×D4×C22⋊C4, C2×D3×#2433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 327739);