Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #88941 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#88942 |
| Sylow | C33 ⋊ C2×SD16 |
276 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #13165503, #13165504, #13165514, … |
| maximal normal subgroup of | #13165503, #13165504, #13165514, … |
| maximal quotient of | #13167409, #13167415, #13167425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 4316);