Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C3⋊#1113)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #10620154⋊C3 |
| derived | C34 ⋊ C2×C3×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
605 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,e^a=e^2,g^a=g^2,h^a=h^2,e^b=e^2,f^b=f^2,g^c=gh102 conjugacy classes — view the full character table.
| maximal subgroup of | #72229111, #72259582, #72260018 |
| maximal normal subgroup of | #72259582, #72260018 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3125);