Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C32 ⋊ #487 |
117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bdef,g^a=g^2h^2,h^a=g^2,c^b=ce,d^b=df,g^b=gh^2,h^b=h^2,g^d=g^2h,h^d=gh,g^f=g^2,h^f=h^227 conjugacy classes — view the full character table.
| maximal subgroup of | #11779557, #11779652, #11779937, … |
| maximal normal subgroup of | #11779557, #11779652, #11779937, … |
| maximal quotient of | #11786042, #11789783, #11790629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8286);