Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#5773 |
| Fitting | C3×C4×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ C4×#575 |
2842 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#575, #72258784 |
| maximal normal subgroup of | C4×D3×#575, #72258784 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033648);