Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D3×#354 |
| Fitting | C2×C3×#354 ⋊ C2 |
| Sylow | C3 ⋊ C22×#354 |
1502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2127, D3×#13349, D3×#13348, … |
| maximal normal subgroup of | C2×D3×#2127, D3×#13349, D3×#13348, … |
| maximal quotient of | D3×#12694, C2×D3×#1393 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322341);