Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#1088 |
| Fitting | D4×H(3,𝔽3) ⋊ C4 |
| Sylow | H(3,𝔽3) ⋊ C4×D4 |
249 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 249 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#6249, #13146635, #13146637, … |
| maximal normal subgroup of | D4⋊#6249, #13146635, #13146637, … |
| maximal quotient of | #13147325, #13147326, #13147327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 2417);