Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C9×#131 ⋊ C2 |
| Sylow | C9 ⋊ #568 |
387 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 387 conjugacy classes of subgroups — too many to draw. Only its 175 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|d^2=e,e^2=f,g^3=h,d^a=df,g^a=g^2h^2,h^a=h^2,c^b=cf114 conjugacy classes — view the full character table.
| maximal subgroup of | #11861130, #11861139, #11861184, … |
| maximal normal subgroup of | #11861130, #11861139, #11861184, … |
| maximal quotient of | #11857215, #11857288, #11857291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1734);