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 ⋊ #104 |
152 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 47 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=c,d^2=e,g^3=h,b^a=bd,c^a=ce,d^a=de,g^a=g^2h^2,h^a=h^2,f^b=f^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63364, #13137284, #13138353, … |
| maximal normal subgroup of | D3×#63364, #13137284, #13138353, … |
| maximal quotient of | #13134924, #13134928, #13134930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 227);