Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| direct product | C2×C4×D3×#41 |
| Fitting | C2×C3×C4×#41 ⋊ C2 |
| Sylow | C3 ⋊ C22×C4×#41 |
12878 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#575, C2×D3×D4×#41, D3×#34258, … |
| maximal normal subgroup of | C4×D3×#575, C2×D3×D4×#41, D3×#34258, … |
| maximal quotient of | D3×#60207, D3×#60208, C2×D3×#2339 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076139);