Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic27 |
| Sylow | C27 ⋊ C4×D4 |
188 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13134261, #13134264, #13134266, … |
| maximal normal subgroup of | #13134261, #13134264, #13134266, … |
| maximal quotient of | C22⋊C4×Dic27, #13134453, #13134454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 150);