Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#87167 |
| Fitting | C2×C3×#568 ⋊ C2 |
| Sylow | C3 ⋊ C2×#3585 |
11138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#3585, C2×#10826601, C2×#10826602, … |
| maximal normal subgroup of | C2×D3×#3585, C2×#10826601, C2×#10826602, … |
| maximal quotient of | #72228385, #72253933, C22×#87167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083410);