Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3753 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#3753 |
| Fitting | C2×C33×D4 ⋊ C2 |
| Sylow | C33 ⋊ C2×D8 |
672 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 672 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×#10591400, C3×#10591429, C3×#10591404, … |
| maximal normal subgroup of | C3×#10591400, C3×#10591429, C3×#10591404, … |
| maximal quotient of | C2×C3×#63634, C2×C3×#63636, C3×#10592666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3853);