Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #496 |
342 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 342 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=f,d^2=f,b^a=be,c^a=cd,d^a=df,h^a=h^2,c^b=cdef,d^b=df,g^b=g^2,d^c=df54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5176, D3×#5154, #11874348, … |
| maximal normal subgroup of | D3×#5176, D3×#5154, #11874348, … |
| maximal quotient of | #11782633, #11782645, #11782673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3357);