Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C4⋊#6258 |
| Fitting | C22×C32×C4 ⋊ D3 |
279 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^3,3^3,2^2|b^2=c,b^a=bc,d^a=d^2,e^a=e^2,g^a=h,h^a=g,e^d=ef,g^d=h,h^d=gh58 conjugacy classes — view the full character table.
| maximal subgroup of | #13146287, #13146289, #13146291, … |
| maximal normal subgroup of | #13146287, #13146289, #13146291, … |
| maximal quotient of | C4⋊#88610, C4⋊#88611, #13147009, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2349);