Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #443 |
227 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 227 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) = 96 |
Polycyclic presentation:
2^6,3^2|b^2=d,c^2=d,d^2=f,c^a=cde,e^a=ef,h^a=h^2,g^b=g^2,e^c=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4824, D3×#5144, C2×#10590975, … |
| maximal normal subgroup of | D3×#4824, D3×#5144, C2×#10590975, … |
| maximal quotient of | #11777150, #11777191, #11777204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2857);