Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
| direct product | Q16×C3⋊D9 |
| Fitting | C3×C9×Q16 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×Q16 |
300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #13139263, #13139268, #13139271, … |
| maximal normal subgroup of | #13139263, #13139268, #13139271, … |
| maximal quotient of | #13143962, #13143964, #13143966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1770);