Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #504 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=d,d^2=e,e^2=f,g^3=h^2,g^a=g^2h,h^a=h^2,c^b=cf120 conjugacy classes — view the full character table.
| maximal subgroup of | #11797546, #11797555, #11797582, … |
| maximal normal subgroup of | #11797546, #11797555, #11797582, … |
| maximal quotient of | #11795878, #11795998, #11797017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 702);