Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C9⋊(#95⋊C3) |
| Fitting | C9×#95 ⋊ C3 |
| Sylow | #95 ⋊ 3−1+2 |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^3,2^5|b^3=c,d^2=g,e^2=f,b^a=bc,d^a=de,e^a=dfh,f^a=g,g^a=fgh,e^d=eh76 conjugacy classes — view the full character table.
| maximal subgroup of | #13136796, #13136798, #13136800, … |
| maximal normal subgroup of | #13136796, #13136798, #13136800, … |
| maximal quotient of | C9⋊(#338⋊C3), C2×C9⋊(#95⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 304);