Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C9×#106 ⋊ C2 |
| Sylow | C9 ⋊ #427 |
171 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 171 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=e,c^2=d,e^2=f,g^3=h^2,c^a=cf,g^a=g^2h,h^a=h^2,c^b=cef,e^c=ef84 conjugacy classes — view the full character table.
| maximal subgroup of | #11796841, #11797116, D9×#427, … |
| maximal normal subgroup of | #11796841, #11797116, D9×#427, … |
| maximal quotient of | #11776795, #11776906, #11777026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 422);