Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ #519 |
610 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=ef,c^2=f,d^2=f,d^a=df,h^a=h^2,c^b=cf,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #11785949, #11788548, #11857579, … |
| maximal normal subgroup of | #11785949, #11788548, #11857579, … |
| maximal quotient of | #11800887, #11800949, #11800950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7221);