Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C9 ⋊ C2 |
| Sylow | C9 ⋊ #459 |
210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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|b^2=e,d^2=f,g^3=h^2,b^a=be,c^a=cd,d^a=df,g^a=g^2h,h^a=h^2,d^c=df99 conjugacy classes — view the full character table.
| maximal subgroup of | #11778886, #11778892, #11778951, … |
| maximal normal subgroup of | #11778886, #11778892, #11778951, … |
| maximal quotient of | #11780787, #11780882, #11780947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 580);