Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #356 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^2,h^a=h^2,c^b=ce,d^b=df,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | #11772781, #11772784, #11772788, … |
| maximal normal subgroup of | #11772781, #11772784, #11772788, … |
| maximal quotient of | #11771400, #11771475, #11771834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1296);