Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #64127⋊C3 |
| Fitting | Q16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #137 |
228 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 61 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:
2^3,3,2^2,3^2|b^2=f,c^2=f,e^2=f,c^a=cf,g^a=g^2,h^a=h^2,c^b=ce,e^b=ef,e^c=ef,g^d=gh61 conjugacy classes — view the full character table.
| maximal subgroup of | #13150001, #13150002, #13150004, … |
| maximal normal subgroup of | #13150001, #13150002, #13150004, … |
| maximal quotient of | #10592517⋊C3, #10592490⋊C3, #10592493⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1531);