Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C32 ⋊ #385 |
506 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|b^2=f,c^2=d,b^a=be,h^a=h^2,c^b=cf,g^b=g^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4989, #11801264, D3×#5210, … |
| maximal normal subgroup of | D3×#4989, #11801264, D3×#5210, … |
| maximal quotient of | #11773163, #11773240, #11773243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3159);