Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #444 |
230 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|b^2=d,c^2=e,d^2=f,c^a=cde,e^a=ef,h^a=h^2,c^b=cf,g^b=g^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4823, #11861051, D3×#4717, … |
| maximal normal subgroup of | D3×#4823, #11861051, D3×#4717, … |
| maximal quotient of | #11777282, #11777284, #11777323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2224);