Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#3775 |
| Sylow | C33 ⋊ C2×SD16 |
276 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#3775, #13165498, #13165511, … |
| maximal normal subgroup of | Dic3×#3775, #13165498, #13165511, … |
| maximal quotient of | C3×#10593359, C3×#10593366, C3×#10593376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4260);