Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ #327 |
227 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 52 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=c,b^2=cde,d^2=ef,b^a=bd,d^a=de,h^a=h^2,c^b=cf,d^b=df,g^b=g^275 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4451, #11774930, C2×#10589151, … |
| maximal normal subgroup of | D3×#4451, #11774930, C2×#10589151, … |
| maximal quotient of | #11770660, #11770676, #11771053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1033);