Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C22×#5244 |
| Fitting | C22×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C22×B(4,𝔽2) |
7014 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 7014 conjugacy classes of subgroups — too many to draw. Only its 827 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72247581, C22×D3×B(4,𝔽2), #72247726, … |
| maximal normal subgroup of | #72247581, C22×D3×B(4,𝔽2), #72247726, … |
| maximal quotient of | C2×#10826768, C2×#10949248, #72248907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1036281);