Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #344 |
214 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=c,d^2=f,b^a=be,c^a=cf,e^a=ef,h^a=h^2,d^b=df,e^b=ef,g^b=g^278 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4533, #11783451, C2×#10589170, … |
| maximal normal subgroup of | D3×#4533, #11783451, C2×#10589170, … |
| maximal quotient of | #11770826, #11770844, #11770864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1052);