Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C32×Q8 ⋊ C22 |
| Sylow | C32 ⋊ #455 |
342 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 342 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) = 48 |
Polycyclic presentation:
2^6,3^2|c^2=f,d^2=f,e^2=f,c^a=ce,e^a=ef,h^a=h^2,c^b=cd,d^b=df,g^b=g^2,d^c=df,e^c=ef48 conjugacy classes — view the full character table.
| maximal subgroup of | #11772759, #11798590, #11798654, … |
| maximal normal subgroup of | #11772759, #11798590, #11798654, … |
| maximal quotient of | #11778218, #11778251, #11778402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3540);