Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #64151⋊C3 |
| Fitting | C2×Q8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #137 |
248 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 67 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=ce,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf,e^c=ef,g^d=gh73 conjugacy classes — view the full character table.
| maximal subgroup of | #13140928, #13140930, #13140952, … |
| maximal normal subgroup of | #13140928, #13140930, #13140952, … |
| maximal quotient of | #10592663⋊C3, #10592670⋊C3, #10592665⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1636);