Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #329 |
160 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|b^2=c,c^2=f,d^2=ef,b^a=bd,c^a=ce,d^a=def,h^a=h^2,d^b=df,g^b=g^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4464, #11775669, D3×#4540, … |
| maximal normal subgroup of | D3×#4464, #11775669, D3×#4540, … |
| maximal quotient of | #11770659, #11770691, #11771071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 968);