Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊(C3⋊#622) |
| Sylow | C33 ⋊ C4⋊C8 |
168 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 168 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) = 96 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=g,g^a=f^2,h^a=h^2,f^c=f^2,g^c=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13154767, #13154768, #13154771, … |
| maximal normal subgroup of | #13154767, #13154768, #13154771, … |
| maximal quotient of | C4⋊(C3⋊#3708), #13157187, #13157189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3068);