Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (((C3⋊D3)⋊C3)⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #10619883⋊C3 |
| derived | C3×H(3,𝔽3) ⋊ C2×C3×C4 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C2×C4 |
388 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,f^a=f^2,g^a=g^2,h^a=h^2,e^b=e^2,h^b=h^2,f^c=fg,f^e=fh78 conjugacy classes — view the full character table.
| maximal subgroup of | #72213798, #72219727, #72219729, … |
| maximal normal subgroup of | #72213798, #72219727, #72219729 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1193);