Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (#272⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #92211⋊C4 |
| derived, Sylow | H(3,𝔽3)⋊C9 ⋊ C2×C4 |
271 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,e^3=g,e^a=e^2g^2,f^a=f^2,g^a=g^2,h^a=h^2,d^b=d^2,f^b=f^2h,e^d=ef,f^d=fh78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 186);