Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C9×M32 ⋊ C2 |
| Sylow | C9 ⋊ #350 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=c,c^2=e,d^2=f,e^2=f,g^3=h^2,b^a=bd,d^a=df,g^a=g^2h,h^a=h^2,d^b=df108 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#350, C2×#10588192, #11796098, … |
| maximal normal subgroup of | D9×#350, C2×#10588192, #11796098, … |
| maximal quotient of | #11771347, #11771447, #11771525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 74);