Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #451 |
321 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^2=f,d^2=f,b^a=bd,d^a=df,h^a=h^2,c^b=ce,d^b=df,g^b=g^269 conjugacy classes — view the full character table.
| maximal subgroup of | #11778254, #11778257, #11778259, … |
| maximal normal subgroup of | #11778254, #11778257, #11778259, … |
| maximal quotient of | #11778257, #11778370, #11778709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3067);