Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C32×#100 ⋊ C2 |
| Sylow | C32 ⋊ #413 |
450 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 99 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=d,d^2=f,b^a=bf,g^a=g^2,h^a=h^2,c^b=ce,d^b=df,e^c=ef66 conjugacy classes — view the full character table.
| maximal subgroup of | #11772587, #11783840, #11786646, … |
| maximal normal subgroup of | #11772587, #11783840, #11786646, … |
| maximal quotient of | #11773747, #11773775, #11773885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4326);