Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#88652 |
| Sylow | H(3,𝔽3) ⋊ C2×#41 |
628 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #13138057, #13138058, #13138059, … |
| maximal normal subgroup of | #13138057, #13138058, #13138059, … |
| maximal quotient of | #13147750, #13147753, #13147760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2453);