Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #63369⋊C3 |
| Fitting | C4⋊C4×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ #102 |
163 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 163 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^2,3,2^3,3^2|b^2=d,e^2=f,g^3=h,b^a=be,e^a=ef,g^a=g^2h^2,h^a=h^2,e^b=ef,g^c=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #10588466⋊C3, #10588440⋊C3, #10588442⋊C3, … |
| maximal normal subgroup of | #10588466⋊C3, #10588440⋊C3, #10588442⋊C3, … |
| maximal quotient of | #10588129⋊C3, #10588159⋊C3, #10588162⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 363);