Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#3771 |
| Sylow | C32 ⋊ C4⋊C16 |
65 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bd,g^a=g^2h^2,h^a=g^2,g^c=g^2h,h^c=gh,g^e=g^2,h^e=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#3771, #11771540, Q8⋊#3771, … |
| maximal normal subgroup of | D4⋊#3771, #11771540, Q8⋊#3771, … |
| maximal quotient of | #11772170, #11772213, #11772268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5144);