Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10619537⋊C3 |
| Sylow | #6891 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (((C3⋊D3)⋊C9)⋊C2)⋊C3 |
| commutator, cosocle | C2×C32⋊C9 | C22×C3 |
| Frattini, socle | C2×C32 | C3×D32 |
| Fitting | C2×#6891 | C22 |
| hypocenter | C32⋊C9 | C3×D4 |
| LCS | G ▷ C2×C32⋊C9 ▷ C32⋊C9 | |
| UCS | C1 ◁ C2 | |
348 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 39 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^3=h,b^a=bd,f^a=f^2h^2,g^a=g^2,h^a=h^2,e^b=e^2,g^b=g^2,f^c=fh^2,f^e=fg69 conjugacy classes — view the full character table.
| maximal subgroup of | #72229239, #72259310, #72259315, … |
| maximal normal subgroup of | #72259310, #72259315, #72259326 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1205);