Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C3×C9×Q16 ⋊ C2 |
| Sylow | C3×C9 ⋊ SD32 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=de,d^2=e,f^3=h,b^a=bc,c^a=cd,d^a=de,f^a=f^2h^2,g^a=g^2,h^a=h^2,c^b=cd,d^b=de102 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63387, #13139254, #13139257, … |
| maximal normal subgroup of | D3×#63387, #13139254, #13139257, … |
| maximal quotient of | #13135807, #13135808, #13135956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 534);