Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C33 ⋊ #108 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^2=cd,c^2=e,b^a=bc,f^a=g,g^a=f^2,h^a=h^2,c^b=ce,d^b=de,f^b=fg^2,g^b=f^2g^2,f^c=f^2,g^c=g^236 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#63748, #13165831, #13165832, … |
| maximal normal subgroup of | D3×#63748, #13165831, #13165832, … |
| maximal quotient of | #13155156, #13155158, #13155175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2777);