Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #63377⋊C3 |
| Sylow | 3−1+2 ⋊ #106 |
119 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^2,3,2^3,3^2|a^2=d,b^2=e,e^2=f,g^3=h,b^a=be,e^a=ef,g^a=g^2h^2,h^a=h^2,g^c=gh106 conjugacy classes — view the full character table.
| maximal subgroup of | #10588171⋊C3, #10588190⋊C3, #10588194⋊C3, … |
| maximal normal subgroup of | #10588171⋊C3, #10588190⋊C3, #10588194⋊C3, … |
| maximal quotient of | #10588134⋊C3, #10588190⋊C3, #10588229⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 404);