Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #126 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^5,3^3|b^2=d,c^2=e,b^a=be,c^a=cde,f^a=f^2,g^a=g^2,g^f=gh106 conjugacy classes — view the full character table.
| maximal subgroup of | #13147791, #13147794, #13147799, … |
| maximal normal subgroup of | #13147791, #13147794, #13147799, … |
| maximal quotient of | #13143721, #13143723, #13143725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1689);