Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C33 ⋊ #108 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^5,3^3|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^2,g^a=f^2g,h^a=h^2,f^b=f^2g^2,g^b=f^2g,f^c=f^2,g^c=g^254 conjugacy classes — view the full character table.
| maximal subgroup of | #13165116, #13165134, D3×#63733, … |
| maximal normal subgroup of | #13165116, #13165134, D3×#63733, … |
| maximal quotient of | #13155085, #13155086, #13155095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2754);