Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C32 ⋊ #482 |
237 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 60 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=ef,e^2=f,b^a=bf,c^a=cdf,h^a=h^2,c^b=ce,e^b=ef,g^b=g^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4737, #11869438, C2×#10590705, … |
| maximal normal subgroup of | D3×#4737, #11869438, C2×#10590705, … |
| maximal quotient of | #11785827, #11786514, #11787348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2587);