Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6295 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#88809 |
| Sylow | C33 ⋊ C2×M16 |
386 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #13154997, #13155002, #13155004, … |
| maximal normal subgroup of | #13154997, #13155002, #13155004, … |
| maximal quotient of | #13161476, #13161479, #13161494, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3625);