Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #485 |
171 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 171 conjugacy classes of subgroups — too many to draw. Only its 31 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|a^2=f,b^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^2,c^b=cf,d^b=df,g^b=h,h^b=g,g^d=g^2,h^d=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593501, #11869532, #11869721, … |
| maximal normal subgroup of | C2×#10593501, #11869532, #11869721, … |
| maximal quotient of | #11785832, #11786526, #11787295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5383);