Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #509 |
159 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|c^2=e,d^2=ef,e^2=f,b^a=bd,c^a=ce,d^a=de,e^a=ef,g^a=g^2,c^b=cef,d^b=de,e^b=ef,g^b=h,h^b=g,g^d=g^2,h^d=h^230 conjugacy classes — view the full character table.
| maximal subgroup of | #11798288, #11798289, #11798370, … |
| maximal normal subgroup of | #11798288, #11798289, #11798370, … |
| maximal quotient of | #11796696, #11796722, #11797240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5159);