Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #441 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=ef,c^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf102 conjugacy classes — view the full character table.
| maximal subgroup of | #11797907, #11797913, #11797926, … |
| maximal normal subgroup of | #11797907, #11797913, #11797926, … |
| maximal quotient of | #11777310, #11777669, #11777925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4297);