Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Sylow | C33 ⋊ #117 |
560 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^3|a^2=e,c^2=d,h^a=h^2,c^b=ce,f^b=f^2,g^b=g^2126 conjugacy classes — view the full character table.
| maximal subgroup of | #13167911, #13167915, #13167931, … |
| maximal normal subgroup of | #13167911, #13167915, #13167931, … |
| maximal quotient of | #13159503, #13159514, #13159563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3431);