Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C32 ⋊ AΣL(1,𝔽16) |
182 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^6,3^2|b^2=d,d^2=f,b^a=bc,d^a=de,g^a=g^2,c^b=ce,e^b=ef,g^b=h,h^b=g,d^c=df,g^c=g^2,h^c=h^233 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590057, #11796156, #11796219, … |
| maximal normal subgroup of | C2×#10590057, #11796156, #11796219, … |
| maximal quotient of | #11771371, #11771499, #11771794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1939);