Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C33×C8 ⋊ C22 |
| Sylow | C33 ⋊ AGL(1,ℤ/8) |
496 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 92 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|c^2=d,d^2=e,c^a=ce,h^a=h^2,c^b=cd,d^b=de,f^b=f^2,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63794, #13167740, #13167784, … |
| maximal normal subgroup of | D3×#63794, #13167740, #13167784, … |
| maximal quotient of | #13159544, #13159545, #13159677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3282);