Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C3×C4 |
| unambiguous semidirect product | #64135⋊C3 |
| Sylow | H(3,𝔽3) ⋊ #117 |
320 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 117 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:
2^3,3,2^2,3^2|a^2=e,b^2=f,c^a=cf,g^a=g^2,h^a=h^2,g^d=gh124 conjugacy classes — view the full character table.
| maximal subgroup of | #13135158, #13135164, #13135173, … |
| maximal normal subgroup of | #13135158, #13135164, #13135173, … |
| maximal quotient of | #10592624⋊C3, #10592625⋊C3, #10592631⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1564);