Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C9 ⋊ #440 |
180 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 79 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|a^2=d,c^2=f,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×#440, C2×#10588844, #11860180, … |
| maximal normal subgroup of | D9×#440, C2×#10588844, #11860180, … |
| maximal quotient of | SD16⋊(C9⋊C8), #11777569, #11777713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 726);