Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C9×C4⋊C8 ⋊ C2 |
| Sylow | C9 ⋊ #331 |
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=c,c^2=e,d^2=f,g^3=h^2,b^a=bd,c^a=ce,d^a=df,g^a=g^2h,h^a=h^2,d^b=def99 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#331, C2×#10588163, #11776120, … |
| maximal normal subgroup of | D9×#331, C2×#10588163, #11776120, … |
| maximal quotient of | #11770651, #11771078, #11772005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 45);