Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C9×#103 ⋊ C2 |
| Sylow | C9 ⋊ #419 |
225 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 69 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=f,c^2=d,e^2=f,g^3=h^2,c^a=cf,g^a=g^2h,h^a=h^2,c^b=ce,e^b=ef,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#419, C2×#10588482, #11857935, … |
| maximal normal subgroup of | D9×#419, C2×#10588482, #11857935, … |
| maximal quotient of | #11774325, #11774512, #11774698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 364);