Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C9⋊#338 |
| Sylow | C9 ⋊ #338 |
129 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=f,d^2=f,e^2=f,g^3=h^2,b^a=be,d^a=df,g^a=g^2h,h^a=h^2,c^b=cf102 conjugacy classes — view the full character table.
| maximal subgroup of | #11771748, #11771751, #11771765, … |
| maximal normal subgroup of | #11771748, #11771751, #11771765, … |
| maximal quotient of | #11770718, #11770721, #11770995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 115);