Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3×C9 ⋊ #103 |
152 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=cd,c^2=e,g^3=h,b^a=bc,c^a=ce,g^a=g^2h^2,h^a=h^2,f^b=f^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #13137078, #13137079, #13137080, … |
| maximal normal subgroup of | #13137078, #13137079, #13137080, … |
| maximal quotient of | #13134924, #13134938, #13134940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 243);