Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#869 |
| Sylow | C33 ⋊ C4⋊Q8 |
528 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10589092, C3×#10589093, C3×#10589095, … |
| maximal normal subgroup of | C3×#10589092, C3×#10589093, C3×#10589095, … |
| maximal quotient of | C32×#4656, C32×#4661, C32×#4680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3705);