Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#68705 |
| Fitting | C2×C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ C2×#1911 |
1974 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#1911, C2×#10826748, C2×#10826745, … |
| maximal normal subgroup of | C2×D3×#1911, C2×#10826748, C2×#10826745, … |
| maximal quotient of | #72253530, #72254854 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 171559);