Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C9 ⋊ #433 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=e,d^2=f,g^3=h^2,c^a=ce,g^a=g^2h,h^a=h^2,c^b=cf108 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#433, C2×#10588678, #11858852, … |
| maximal normal subgroup of | D9×#433, C2×#10588678, #11858852, … |
| maximal quotient of | #11783507, #11783596, #11784212, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 560);