Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88421 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#88423 |
| Sylow | C3×C9 ⋊ C2×SD16 |
226 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #13137228, #13137236, #13137237, … |
| maximal normal subgroup of | #13137228, #13137236, #13137237, … |
| maximal quotient of | #13137040, #13137050, #13137058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 853);