Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #427 |
342 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=f,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #11772397, #11772400, #11772405, … |
| maximal normal subgroup of | #11772397, #11772400, #11772405, … |
| maximal quotient of | #11776805, #11776916, #11777036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4687);