Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×#108 ⋊ C2 |
| Sylow | C32 ⋊ #361 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,d^b=def,e^b=ef72 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#361, C2×#10589361, D3×#4495, … |
| maximal normal subgroup of | C3⋊D3×#361, C2×#10589361, D3×#4495, … |
| maximal quotient of | #11771600, #11771882, #11772058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1243);