Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #358 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=f,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^2,c^b=ce,e^b=ef,g^b=h,h^b=g,g^c=g^2,h^c=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590062, #11796630, #11796662, … |
| maximal normal subgroup of | C2×#10590062, #11796630, #11796662, … |
| maximal quotient of | #11771596, #11771878, #11772087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1944);