Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×#95 ⋊ C2 |
| Sylow | C32 ⋊ #327 |
270 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 270 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) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=c,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^2,h^a=h^2,d^b=df99 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#327, C2×#10589317, D3×#4451, … |
| maximal normal subgroup of | C3⋊D3×#327, C2×#10589317, D3×#4451, … |
| maximal quotient of | #11770652, #11770671, #11771045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1199);