Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #64110⋊C3 |
| Fitting | C2×C8×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #131 |
239 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 83 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|c^2=e,e^2=f,b^a=bf,g^a=g^2,h^a=h^2,g^d=gh124 conjugacy classes — view the full character table.
| maximal subgroup of | #13135086, #13135093, #10589374⋊C3, … |
| maximal normal subgroup of | #13135086, #13135093, #10589374⋊C3, … |
| maximal quotient of | C8×#634⋊C3, #10592378⋊C3, C8×C4⋊((C3⋊D3)⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1469);