Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ #418 |
570 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^2,h^a=h^2,c^b=cf102 conjugacy classes — view the full character table.
| maximal subgroup of | #11784959, #11784965, #11784977, … |
| maximal normal subgroup of | #11784959, #11784965, #11784977, … |
| maximal quotient of | #11774306, #11774494, #11774680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4712);