Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C3×C9 ⋊ M32 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|a^2=c,c^2=d,d^2=e,f^3=h,b^a=be,f^a=f^2h^2,g^a=g^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | #13134987, #13134988, #13134990, … |
| maximal normal subgroup of | #13134987, #13134988, #13134990, … |
| maximal quotient of | #13135740, C4⋊(C3⋊(C9⋊C16)), #13135926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 501);