Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊(C3⋊#226) |
176 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 176 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) = 192 |
Polycyclic presentation:
2^3,3^2,2^3|a^2=h,b^2=c,f^2=h,g^2=h,b^a=bc,d^a=d^2,e^a=e^2,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh51 conjugacy classes — view the full character table.
| maximal subgroup of | #11920503, #11920508, #11920526, … |
| maximal normal subgroup of | #11920503, #11920508, #11920526, … |
| maximal quotient of | #11920967, #11920968, #11920969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5506);