Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #462 |
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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=f,b^2=e,c^2=f,d^2=f,g^3=h^2,c^a=cd,d^a=df,g^a=g^2h,h^a=h^2,c^b=ce,d^c=df75 conjugacy classes — view the full character table.
| maximal subgroup of | #11779748, #11779754, #11779795, … |
| maximal normal subgroup of | #11779748, #11779754, #11779795, … |
| maximal quotient of | #11781051, #11781131, #11781196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 645);