Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| unambiguous semidirect product | #64361⋊C3 |
| Fitting | C2×D4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ H(5,𝔽2) |
635 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 635 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3,2,3^2|d^a=df,g^a=g^2,h^a=h^2,c^b=cf,g^e=gh91 conjugacy classes — view the full character table.
| maximal subgroup of | #13140531, #13140532, #13140567, … |
| maximal normal subgroup of | #13140531, #13140532, #13140567, … |
| maximal quotient of | #10595954⋊C3, #10595957⋊C3, #10595961⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2582);