Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #64138⋊C3 |
| Fitting | C22×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #123 |
327 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 77 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|c^2=f,b^a=bf,c^a=ce,g^a=g^2,h^a=h^2,g^d=gh106 conjugacy classes — view the full character table.
| maximal subgroup of | #13140249, #10592752⋊C3, #13150683, … |
| maximal normal subgroup of | #13140249, #10592752⋊C3, #13150683, … |
| maximal quotient of | #10592632⋊C3, #10592639⋊C3, #10592651⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1567);