Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| isoclinism | isoclinic class of #634⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C4⋊((C3⋊Dic3)⋊C3) |
| unambiguous semidirect product | (C2×C4⋊(C3⋊Dic3))⋊C3 |
| Sylow | H(3,𝔽3) ⋊ C2×C4⋊C4 |
376 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 376 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.
| maximal subgroup of | #13135162, #13135170, #13135172, … |
| maximal normal subgroup of | #13135162, #13135170, #13135172, … |
| maximal quotient of | C2×C4⋊((C3⋊(C3⋊C8))⋊C3), #10592623⋊C3, C4×C4⋊((C3⋊Dic3)⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1563);