Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #477 |
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=ef,c^2=ef,d^2=f,c^a=ce,g^a=g^2,h^a=h^2,c^b=cd,d^b=df,d^c=df75 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#477, C2×#10592574, D3×#4875, … |
| maximal normal subgroup of | C3⋊D3×#477, C2×#10592574, D3×#4875, … |
| maximal quotient of | #11785202, #11786860, #11786872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4456);