Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C23×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ #99 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^5,3^3|a^2=c,b^a=bd,d^a=de,f^a=fg,g^a=fg^2h^2,c^b=ce,f^c=f^2,g^c=g^2h,g^f=gh49 conjugacy classes — view the full character table.
| maximal subgroup of | #13136713, #13136714, #13136887, … |
| maximal normal subgroup of | #13136713, #13136714, #13136887, … |
| maximal quotient of | #13136934, #13136937, #13136940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 759);