Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #500 |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=d,c^2=d,e^2=f,c^a=ce,g^a=g^2,h^a=h^2,c^b=cd,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11780084, #11780087, #11780090, … |
| maximal normal subgroup of | #11780084, #11780087, #11780090, … |
| maximal quotient of | #11786225, #11790121, #11791679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4659);