Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C23×D3×C22⋊C4 |
| Fitting | C23×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C24×C22⋊C4 |
43678 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C23×D3×#120, D3×#10735, C2×D3×#1898, … |
| maximal normal subgroup of | C23×D3×#120, D3×#10735, C2×D3×#1898, … |
| maximal quotient of | C22×D3×#418, C22×D3×#407, C2×D3×D4×C22⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076118);