Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #494 |
366 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=e,c^2=df,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^2,h^a=h^2150 conjugacy classes — view the full character table.
| maximal subgroup of | #11772017, #11772024, #11772075, … |
| maximal normal subgroup of | #11772017, #11772024, #11772075, … |
| maximal quotient of | #11782473, #11782556, #11782601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4280);