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 |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=f,c^2=ef,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^2,c^b=ce,e^b=ef,g^b=h,h^b=g,g^d=g^2,h^d=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #11772026, #11772089, #11781002, … |
| maximal normal subgroup of | #11772026, #11772089, #11781002, … |
| maximal quotient of | #11782491, #11782493, #11782565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5177);