Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C2×C32×M16 ⋊ C2 |
| Sylow | C32 ⋊ #568 |
774 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 259 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,c^a=cf,g^a=g^2,h^a=h^2,d^b=df114 conjugacy classes — view the full character table.
| maximal subgroup of | #11786632, #11786641, #11786651, … |
| maximal normal subgroup of | #11786632, #11786641, #11786651, … |
| maximal quotient of | #11857219, #11857222, #11857286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8098);