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 |
292 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 50 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=e,b^2=d,h^a=h^2,c^b=ce,f^b=g,g^b=f^2,f^d=f^2,g^d=g^254 conjugacy classes — view the full character table.
| maximal subgroup of | #13165457, #13165458, #13166445, … |
| maximal normal subgroup of | #13165457, #13165458, #13166445, … |
| maximal quotient of | #13166281, #13166303, #13166304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4228);