Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #3754⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×#3756⋊C3 |
| unambiguous semidirect product | (C2×#3756)⋊C3 |
| Sylow | H(3,𝔽3) ⋊ C2×Q16 |
248 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
82 conjugacy classes — view the full character table.
| maximal subgroup of | #13140879, #13140880, #13140885, … |
| maximal normal subgroup of | #13140879, #13140880, #13140885, … |
| maximal quotient of | C2×#63634⋊C3, #10592669⋊C3, C2×#63637⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1634);