Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C9 · Schur multiplier (H2) = C25 |
| direct product | C9×#1009 |
| Fitting | C3×C9×#41 ⋊ C2 |
| Sylow | C3×C9 ⋊ H(5,𝔽2) |
538 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 255 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | #13141038, #13141052, #13141055, … |
| maximal normal subgroup of | #13141038, #13141052, #13141055, … |
| maximal quotient of | C9×#5532, C9×#5519, C9×#5521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2602);