Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #63365⋊C3 |
| Fitting | C22⋊C4×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ #99 |
173 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 173 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2^3,3^2|b^2=d,g^3=h,b^a=be,d^a=df,g^a=g^2h^2,h^a=h^2,e^b=ef,g^c=gh73 conjugacy classes — view the full character table.
| maximal subgroup of | #10588420⋊C3, #10588421⋊C3, #10588422⋊C3, … |
| maximal normal subgroup of | #10588420⋊C3, #10588421⋊C3, #10588422⋊C3, … |
| maximal quotient of | #10588128⋊C3, #10588129⋊C3, #10588145⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 347);