Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3^2,2^2|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=h,h^a=g,g^e=h,h^e=gh54 conjugacy classes — view the full character table.
| maximal subgroup of | #11920580, #11920582, #11920588, … |
| maximal normal subgroup of | #11920580, #11920582, #11920588, … |
| maximal quotient of | #11920969, #11920970, #11920972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5514);