Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #456 |
426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=f,c^2=f,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^2,h^a=h^2,d^b=df,e^b=ef,e^c=ef84 conjugacy classes — view the full character table.
| maximal subgroup of | #11772786, #11798754, #11798757, … |
| maximal normal subgroup of | #11772786, #11798754, #11798757, … |
| maximal quotient of | #11778277, #11778322, #11778355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4827);