Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C8×Q8 |
306 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=d,c^2=de,e^2=f,g^a=g^2,h^a=h^2,c^b=cd120 conjugacy classes — view the full character table.
| maximal subgroup of | #11771683, #11777171, #11777183, … |
| maximal normal subgroup of | #11771683, #11777171, #11777183, … |
| maximal quotient of | #11784242, #11784254, #11788933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4411);