Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C9×#108 ⋊ C2 |
| Sylow | C9 ⋊ #444 |
156 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=d,d^2=f,e^2=f,g^3=h^2,b^a=be,e^a=ef,g^a=g^2h,h^a=h^2,c^b=ce,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11797903, #11797915, #11797949, … |
| maximal normal subgroup of | #11797903, #11797915, #11797949, … |
| maximal quotient of | #11777254, #11777303, #11777336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 456);