Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #490 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=d,e^2=f,b^a=bf,c^a=cde,g^a=g^2,h^a=h^2,c^b=cd,e^c=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | #11771989, #11772870, #11772878, … |
| maximal normal subgroup of | #11771989, #11772870, #11772878, … |
| maximal quotient of | #11786071, #11789896, #11790755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4652);