Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C32×C8 ⋊ C22 |
| Sylow | C32 ⋊ #447 |
421 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 421 conjugacy classes of subgroups — too many to draw. Only its 68 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|c^2=df,d^2=f,c^a=cd,d^a=df,h^a=h^2,c^b=cde,d^b=df,g^b=g^263 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5156, D3×#4773, #11863527, … |
| maximal normal subgroup of | D3×#5156, D3×#4773, #11863527, … |
| maximal quotient of | #11778000, #11778113, #11778452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2827);