Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Sylow | C33 ⋊ #101 |
532 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^2,g^a=g^2,h^a=h^2,d^b=de141 conjugacy classes — view the full character table.
| maximal subgroup of | #13160111, #13160114, #13160123, … |
| maximal normal subgroup of | #13160111, #13160114, #13160123, … |
| maximal quotient of | #13146012, #13146014, #13146030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2161);