Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C33 |
| direct product | C22⋊C4×C3⋊(C3⋊D3) |
| Fitting | C33×C22⋊C4 ⋊ C2 |
| Sylow | C33 ⋊ C2×C22⋊C4 |
1848 conjugacy classes of subgroups; only the 335 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 335 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | #13159065, #99×C3⋊(C3⋊D3), #13175451, … |
| maximal normal subgroup of | #13159065, #99×C3⋊(C3⋊D3), #13175451, … |
| maximal quotient of | #13163286, #13163287, #13163288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 3888);