Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ #124 |
300 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 54 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,c^2=e,b^a=be,c^a=ce,g^a=g^2,h^a=h^2,c^b=cd,f^b=f^2,h^b=h^2,g^f=gh52 conjugacy classes — view the full character table.
| maximal subgroup of | #13147789, #13147799, #13147802, … |
| maximal normal subgroup of | #13147789, #13147799, #13147802, … |
| maximal quotient of | #13137998, #13138000, #13138010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1122);