Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×C3×D4×D9 |
| Fitting | C2×C3×D4×C9 ⋊ C2 |
| Sylow | C3×C9 ⋊ C22×D4 |
762 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#834, D9×#832, #13140355, … |
| maximal normal subgroup of | D9×#834, D9×#832, #13140355, … |
| maximal quotient of | C2×C3×#63440, C2×C3×#63447, C2×C3×C22⋊C4×D9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2574);