Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C9×#101 ⋊ C2 |
| Sylow | C9 ⋊ #355 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=c,c^2=f,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=def,e^b=ef,d^c=df57 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#355, C2×#10588155, #11796490, … |
| maximal normal subgroup of | D9×#355, C2×#10588155, #11796490, … |
| maximal quotient of | #11771384, #11771459, #11771813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 37);