Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C4⋊C4×(C3⋊D3)⋊C3 |
| unambiguous semidirect product | (C4⋊C4×C3⋊D3)⋊C3 |
| Fitting | C4⋊C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ C2×C4⋊C4 |
348 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13137925, #13137927, #13137936, … |
| maximal normal subgroup of | #13137925, #13137927, #13137936, … |
| maximal quotient of | #10592366⋊C3, #10592348⋊C3, #10592349⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1432);