Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ C4⋊Q8 |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|a^2=e,b^2=e,c^2=e,b^a=bd,c^a=ce,f^a=f^2,g^a=gh,h^a=h^2,c^b=ce,f^b=gh^2,g^b=fh^2,h^b=h^2,f^d=f^2,g^d=g^2h^2,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | #13146168, #13146459, #13146463, … |
| maximal normal subgroup of | #13146168, #13146459, #13146463, … |
| maximal quotient of | #13146513, #13146515, #13146519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2267);