Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#70926 |
| Fitting | C2×C3×#443 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2213 |
790 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2213, #72226024, #72226026, … |
| maximal normal subgroup of | C2×D3×#2213, #72226024, #72226026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323948);