Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C3×C8 ⋊ D3 |
184 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^4,3^2,2^2|b^2=c,c^2=d,b^a=bd,e^a=e^2,f^a=f^2,g^a=h,h^a=g,g^e=h,h^e=gh60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5400, S4×ΓL(1,𝔽25), #11921793, … |
| maximal normal subgroup of | D3×#5400, S4×ΓL(1,𝔽25), #11921793, … |
| maximal quotient of | #11920965, #11920966, #11920974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5516);