Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | C4⋊((C3⋊S4)⋊C3) |
| unambiguous semidirect product | (C4⋊(C3⋊S4))⋊C3 |
| Fitting | C22×C32×C4 ⋊ D3 |
227 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3,2,3^2,2^2|b^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=h,h^a=g,e^c=ef,g^e=h,h^e=gh58 conjugacy classes — view the full character table.
| maximal subgroup of | #13146288, #13146289, #13146294, … |
| maximal normal subgroup of | #13146288, #13146289, #13146294, … |
| maximal quotient of | C4⋊((C3⋊#226)⋊C3), C4⋊((C3⋊GL(2,𝔽3))⋊C3), #10593629⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2308);