Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ AΣL(1,𝔽16) |
282 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^a=bd,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,c^b=ce,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×AΣL(1,𝔽16), C2×#10589402, D3×#4536, … |
| maximal normal subgroup of | C3⋊D3×AΣL(1,𝔽16), C2×#10589402, D3×#4536, … |
| maximal quotient of | #11771364, #11771487, #11771783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1284);