Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #494 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=f,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^2,c^b=ce,d^b=df,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11772087, #11779430, #11779436, … |
| maximal normal subgroup of | #11772087, #11779430, #11779436, … |
| maximal quotient of | #11782485, #11782564, #11782608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2269);