Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q16×C27 ⋊ C2 |
| Sylow | C27 ⋊ SD32 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=e,c^2=de,d^2=e,f^3=g,g^3=h,b^a=bc,c^a=cd,d^a=de,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,c^b=cd,d^b=de102 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D27, #13134419, #13134423, … |
| maximal normal subgroup of | SD32×D27, #13134419, #13134423, … |
| maximal quotient of | #13133986, #13133988, #13134061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 36);