Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #419 |
321 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 86 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|b^2=f,c^2=de,d^2=f,c^a=cf,h^a=h^2,c^b=cd,d^b=df,g^b=g^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4802, #11857866, D3×#5120, … |
| maximal normal subgroup of | D3×#4802, #11857866, D3×#5120, … |
| maximal quotient of | #11774347, #11774534, #11774720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2830);