Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Fitting | C32×#108 ⋊ C2 |
| Sylow | C32 ⋊ #430 |
306 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bf,g^a=g^2,h^a=h^2,c^b=ce,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11799976, #11799985, #11799993, … |
| maximal normal subgroup of | #11799976, #11799985, #11799993, … |
| maximal quotient of | #11776826, #11776832, #11776936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4474);