Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #578⋊C9 |
| Sylow | #578 ⋊ C9 |
127 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^2,3,2,3,2^3|c^3=e,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,d^b=dh,f^c=fg,g^c=f,g^f=gh78 conjugacy classes — view the full character table.
| maximal subgroup of | #3416⋊C9, #3417⋊C9, C2×#578⋊C9, … |
| maximal normal subgroup of | #3416⋊C9, #3417⋊C9, C2×#578⋊C9, … |
| maximal quotient of | #2898⋊C9, #2913⋊C9, #3359⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1444);