Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C27 ⋊ C2 |
| Sylow | C27 ⋊ #104 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^5,3^3|b^2=c,d^2=e,f^3=g,g^3=h,b^a=bd,c^a=ce,d^a=de,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2222 conjugacy classes — view the full character table.
| maximal subgroup of | #13134205, #13134222, #104×D27, … |
| maximal normal subgroup of | #13134205, #13134222, #104×D27, … |
| maximal quotient of | #13133947, #13133948, #13133958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 12);