Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#6171 |
| Fitting | C22×C4×C27 ⋊ C2 |
| Sylow | C27 ⋊ C4×D4 |
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13134225, #6171⋊C8, #13134236, … |
| maximal normal subgroup of | #13134225, #6171⋊C8, #13134236, … |
| maximal quotient of | C4×Dic27⋊C4, #13134437, C4×(C2×D27)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 144);