Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C33 ⋊ #137 |
440 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=e,d^2=e,b^a=bd,d^a=de,h^a=h^2,c^b=ce,d^b=de,f^b=f^2,g^b=g^293 conjugacy classes — view the full character table.
| maximal subgroup of | #13155935, #13155947, #13155951, … |
| maximal normal subgroup of | #13155935, #13155947, #13155951, … |
| maximal quotient of | #13158814, #13158826, #13158845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3342);