Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #67⋊(C3⋊C8) |
| Sylow | C32 ⋊ C8×D4 |
306 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|b^2=d,d^2=f,c^a=ce,h^a=h^2,c^b=ce,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#67⋊C8, D3×D4×C3⋊C8, C8×#3811, … |
| maximal normal subgroup of | D3×#67⋊C8, D3×D4×C3⋊C8, C8×#3811, … |
| maximal quotient of | #11777152, #11777193, #11777202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3032);