Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C4×C8×C9 ⋊ C2 |
| Sylow | C9 ⋊ #433 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=d,d^2=f,g^3=h^2,b^a=bf,c^a=ce,g^a=g^2h,h^a=h^2156 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#433, C2×#10588372, #11858852, … |
| maximal normal subgroup of | D9×#433, C2×#10588372, #11858852, … |
| maximal quotient of | #11783504, #11783599, #11784215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 254);