Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C9×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C9 ⋊ #576 |
402 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 119 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|e^2=f,g^3=h,b^a=bf,g^a=g^2h^2,h^a=h^2,d^b=df,d^c=de,e^c=ef,e^d=ef66 conjugacy classes — view the full character table.
| maximal subgroup of | #11886556, #11886562, #11886568, … |
| maximal normal subgroup of | #11886556, #11886562, #11886568, … |
| maximal quotient of | #11857999, #11858002, #11858575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1758);