Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×C3⋊((C3⋊D3)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| derived | C34 ⋊ C2×C3×C4 |
| Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
899 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 899 conjugacy classes of subgroups — too many to draw. Only its 92 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:
2^2,3,2,3^4|a^2=d,b^2=d,g^a=g^2,e^b=e^2,f^b=f^2,h^b=h^2,f^c=fh126 conjugacy classes — view the full character table.
| maximal subgroup of | #72229111, #72259603, (C3⋊D3)⋊C3×#624, … |
| maximal normal subgroup of | #72259603, (C3⋊D3)⋊C3×#624, #72259784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3067);