Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#69598 |
| Fitting | C2×C3×#386 ⋊ C2 |
| Sylow | C3 ⋊ C2×#1790 |
4402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #72247574, #72247597, C2×D3×#1790, … |
| maximal normal subgroup of | #72247574, #72247597, C2×D3×#1790, … |
| maximal quotient of | C2×#10710963, C2×#10710949, C2×#10710947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168827);