Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×D3×D16 |
| Fitting | C22×C3×D16 ⋊ C2 |
| Sylow | C3 ⋊ C23×D16 |
2590 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 627 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#2177, C22×C3⋊D3×D16, C2×D3×#2263, … |
| maximal normal subgroup of | C2×D3×#2177, C2×D3×#2263, C2×D3×#1419 |
| maximal quotient of | C22×C3⋊D3×D16, C2×D3×#2263 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076041);