Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#74874 |
| Fitting | C2×C3×#386 ⋊ C2 |
| Sylow | C3 ⋊ C2×#2308 |
8142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10974246, C2×#10974247, C2×D3×#2308 |
| maximal normal subgroup of | C2×#10974246, C2×#10974247, C2×D3×#2308 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 328114);