Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #494 |
274 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=f,c^2=f,d^2=f,b^a=be,c^a=ce,h^a=h^2,c^b=cd,d^b=df,g^b=g^2,d^c=df60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5183, #11874212, D3×#5092, … |
| maximal normal subgroup of | D3×#5183, #11874212, D3×#5092, … |
| maximal quotient of | #11782478, #11782480, #11782486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 3508);