Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#101 |
302 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=f,c^2=f,d^2=f,c^a=ce,e^a=ef,g^a=gh,h^a=gh^2,c^b=cf,d^c=df,g^d=g^2,h^d=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | #11772615, #11772622, #101×#157, … |
| maximal normal subgroup of | #11772615, #11772622, #101×#157, … |
| maximal quotient of | #11773736, #11773833, #11773834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5718);