Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #6171⋊C4 |
| Fitting | C22⋊C4×C27 ⋊ C2 |
| Sylow | C27 ⋊ C4×D4 |
188 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|c^2=d,f^3=g,g^3=h,b^a=be,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=ce150 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#6171⋊C4, #13136225, #13136229, … |
| maximal normal subgroup of | C2×#6171⋊C4, #13136225, #13136229, … |
| maximal quotient of | #13134151, #13134155, #13134157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 97);