Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| unambiguous semidirect product | #67⋊(C3⋊Dic3) |
| Sylow | C33 ⋊ C4×D4 |
780 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 178 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:
2^5,3^3|b^2=d,c^a=ce,h^a=h^2,c^b=ce,f^b=f^2,g^b=g^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #13171730, Dic3×#3805, #13171745, … |
| maximal normal subgroup of | #13171730, Dic3×#3805, #13171745, … |
| maximal quotient of | #13160447, #13160458, #13160465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3592);