Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #63628⋊C3 |
| Sylow | H(3,𝔽3) ⋊ Q32 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^2,3,2^3,3^2|a^2=f,b^2=de,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,g^c=gh97 conjugacy classes — view the full character table.
| maximal subgroup of | #13134912, #13134913, #13134917, … |
| maximal normal subgroup of | #13134912, #13134913, #13134917, … |
| maximal quotient of | #10589370⋊C3, #10589369⋊C3, C2×#63628⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 322);