Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ #576 |
804 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 219 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|e^2=f,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf,e^d=ef90 conjugacy classes — view the full character table.
| maximal subgroup of | #11886557, #11886560, #11886566, … |
| maximal normal subgroup of | #11886557, #11886560, #11886566, … |
| maximal quotient of | #11857997, #11858006, #11858573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8188);