Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Fitting | C2×C33×C4 ⋊ C4 |
| Sylow | C33 ⋊ #117 |
292 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=e,c^a=ce,f^a=g,g^a=f^2,h^a=h^2,f^d=f^2,g^d=g^284 conjugacy classes — view the full character table.
| maximal subgroup of | #13154796, #13154797, #13154802, … |
| maximal normal subgroup of | #13154796, #13154797, #13154802, … |
| maximal quotient of | #13173325, #13173326, #13173327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4481);