Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C33 ⋊ #104 |
344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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,b^a=bd,c^a=ce,d^a=de,h^a=h^2,f^b=f^2,g^b=g^2102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63569, #13155421, #13155430, … |
| maximal normal subgroup of | D3×#63569, #13155421, #13155430, … |
| maximal quotient of | #13145507, #13145513, #13145518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2011);