Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C9 ⋊ #501 |
135 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,b^2=e,c^2=d,e^2=f,g^3=h^2,b^a=bf,c^a=cd,g^a=g^2h,h^a=h^2,c^b=ce,e^c=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#501, C2×#10588556, #11875053, … |
| maximal normal subgroup of | D9×#501, C2×#10588556, #11875053, … |
| maximal quotient of | #11786275, #11790160, #11790166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 438);