Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #441 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=f,c^2=f,e^2=f,g^3=h^2,c^a=cf,g^a=g^2h,h^a=h^2,c^b=ce,e^b=ef,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11797909, #11797915, D9×#441, … |
| maximal normal subgroup of | #11797909, #11797915, D9×#441, … |
| maximal quotient of | #11777306, #11777665, #11777921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 746);