Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #354 |
105 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=f,d^2=f,g^3=h^2,b^a=bd,d^a=def,e^a=ef,g^a=g^2h,h^a=h^2,c^b=ce,d^b=df,d^c=df69 conjugacy classes — view the full character table.
| maximal subgroup of | #11772764, #11772767, #11772796, … |
| maximal normal subgroup of | #11772764, #11772767, #11772796, … |
| maximal quotient of | #11771399, #11771462, #11771799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 100);