Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #638⋊A4 |
| Fitting | C24×C32 ⋊ C2×C3 |
336 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3,2^3,3^2|b^a=bd,g^a=g^2,h^a=h^2,e^c=f,f^c=ef,g^c=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | #13164252, #13164253, #13164262, … |
| maximal normal subgroup of | #13164252, #13164253, #13164262, … |
| maximal quotient of | #3750⋊A4, #3752⋊A4, #3754⋊A4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2409);