Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Sylow | C33 ⋊ #108 |
420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,h^a=h^2222 conjugacy classes — view the full character table.
| maximal subgroup of | #13145576, #13145578, #13145588, … |
| maximal normal subgroup of | #13145576, #13145578, #13145588, … |
| maximal quotient of | #13146002, #13146003, #13146098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2156);