Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #63649⋊C3 |
| Sylow | H(3,𝔽3) ⋊ #108 |
125 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 125 conjugacy classes of subgroups — too many to draw. Only its 45 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:
2^2,3,2^3,3^2|a^2=e,b^2=d,d^2=f,e^2=f,b^a=be,g^a=g^2,h^a=h^2,e^b=ef,g^c=gh82 conjugacy classes — view the full character table.
| maximal subgroup of | #13139163, #13139164, #13139174, … |
| maximal normal subgroup of | #13139163, #13139164, #13139174, … |
| maximal quotient of | #10589345⋊C3, #10589346⋊C3, #10589424⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 416);