Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of 3−1+2⋊Q8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(3−1+2⋊C4) |
| unambiguous semidirect product | (C2×C4⋊Dic9)⋊C3 |
| Sylow | 3−1+2 ⋊ C2×C4⋊C4 |
303 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1574);