Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ AΣL(1,𝔽16) |
214 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 38 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=c,c^2=f,b^a=bd,c^a=ce,h^a=h^2,d^b=de,e^b=ef,g^b=g^2,d^c=df48 conjugacy classes — view the full character table.
| maximal subgroup of | #11796145, D3×#4536, C2×#10589173, … |
| maximal normal subgroup of | #11796145, D3×#4536, C2×#10589173, … |
| maximal quotient of | #11771368, #11771494, #11771790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1055);