Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #11757735 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived, Sylow | C3×AΣL(1,𝔽27) ⋊ C2×C4 |
627 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^3,3^5|b^2=c,f^a=f^2,g^a=g^2h,d^b=d^2,e^b=e^2,g^b=g^2,h^b=h^2,f^e=fg,g^f=gh78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1406);