Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #428 |
177 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=e,c^2=e,d^2=f,g^3=h^2,c^a=cd,d^a=df,g^a=g^2h,h^a=h^2,c^b=cf,d^c=df102 conjugacy classes — view the full character table.
| maximal subgroup of | #11786571, #11786574, #11786604, … |
| maximal normal subgroup of | #11786571, #11786574, #11786604, … |
| maximal quotient of | #11776837, #11776947, #11777072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 561);