Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #6872 ⋊ Q8 |
102 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 102 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,e^3=f,f^3=h,b^a=bc,e^a=e^2f^2h^2,f^a=f^2h^2,g^a=g^2,h^a=h^2,d^b=d^2,g^b=g^2h^2,e^d=eg,g^d=gh^275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 192);