Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | #64117⋊C3 |
| Fitting | M16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ AGL(1,ℤ/8) |
258 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^3,3,2^2,3^2|c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf,g^d=gh73 conjugacy classes — view the full character table.
| maximal subgroup of | #13139171, #13139173, #13139178, … |
| maximal normal subgroup of | #13139171, #13139173, #13139178, … |
| maximal quotient of | #10592401⋊C3, #10592413⋊C3, #10592409⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1490);