Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24×C3 |
| unambiguous semidirect product | #64091⋊C3 |
| Fitting | C22⋊C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #120 |
489 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 489 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) = 72 |
Polycyclic presentation:
2^3,3,2^2,3^2|c^2=e,c^a=ce,g^a=g^2,h^a=h^2,c^b=cf,g^d=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13137472, #10592440⋊C3, #13148491, … |
| maximal normal subgroup of | #13137472, #10592440⋊C3, #13148491, … |
| maximal quotient of | #10592355⋊C3, #10592372⋊C3, #10592364⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1389);