Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #6226 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4⋊(C3⋊Dic9) |
| Sylow | C3×C9 ⋊ C2×C4⋊C4 |
460 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 281 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | #13135124, #13135138, #13135141, … |
| maximal normal subgroup of | #13135124, #13135138, #13135141, … |
| maximal quotient of | C2×C4⋊(C3⋊(C9⋊C8)), #13144228, C4×C4⋊(C3⋊Dic9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1781);