Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C9 ⋊ #416 |
237 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 101 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,b^2=f,d^2=f,g^3=h^2,c^a=cd,d^a=df,g^a=g^2h,h^a=h^2,d^c=df108 conjugacy classes — view the full character table.
| maximal subgroup of | #11784061, #11784070, #11784110, … |
| maximal normal subgroup of | #11784061, #11784070, #11784110, … |
| maximal quotient of | #11774231, #11774421, #11774607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 799);