Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| direct product | C3×#64366 |
| Fitting | C33×#41 ⋊ C2 |
| Sylow | C33 ⋊ H(5,𝔽2) |
1156 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1156 conjugacy classes of subgroups — too many to draw. Only its 306 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
171 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10591667, C3×#10591690, #13161355, … |
| maximal normal subgroup of | C3×#10591667, C3×#10591690, #13161355, … |
| maximal quotient of | C3×#10596003, C3×#10595990, C3×#10595992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4636);