Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C32 ⋊ #490 |
240 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|c^2=de,e^2=f,b^a=bd,c^a=ce,e^a=ef,h^a=h^2,c^b=cef,e^b=ef,g^b=g^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11771993, D3×#4764, #11873578, … |
| maximal normal subgroup of | #11771993, D3×#4764, #11873578, … |
| maximal quotient of | #11786077, #11789903, #11789906, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2770);