Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×#80279 |
| Fitting | C2×C3×#453 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3021 |
4934 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3021, #72253954, #72253970, … |
| maximal normal subgroup of | C2×D3×#3021, #72253954, #72253970, … |
| maximal quotient of | #72254868 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036218);