Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#5241 |
| Fitting | C22×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C22×#453 |
5670 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×#453, C2×#10826819, C2×#10826822, … |
| maximal normal subgroup of | C22×D3×#453, C2×#10826819, C2×#10826822 |
| maximal quotient of | C2×#10826822, C2×D3×#5241 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036170);