Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C9 ⋊ #491 |
135 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 135 conjugacy classes of subgroups — too many to draw. Only its 49 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=e,b^2=f,c^2=e,d^2=f,g^3=h^2,b^a=be,c^a=cef,g^a=g^2h,h^a=h^2,c^b=cd,d^b=df,d^c=df72 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#491, C2×#10588477, #11873628, … |
| maximal normal subgroup of | D9×#491, C2×#10588477, #11873628, … |
| maximal quotient of | #11786061, #11789831, #11789834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 359);