Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×C3×#3754 |
| Sylow | C33 ⋊ C2×SD16 |
624 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10591401, C3×#10591439, C3×#10591405, … |
| maximal normal subgroup of | C3×#10591401, C3×#10591439, C3×#10591405, … |
| maximal quotient of | C3×#10592670, C2×C3×#63635, C2×C3×#63637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3855);