Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×#6878 ⋊ C2 |
| Sylow | #6878 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#6878⋊C2 |
| commutator, cosocle | C2×C92 | C22×C3 |
| Frattini | C2×C3×C9 | C2×C3×D3 |
| Fitting | C22×#6878 | C2 |
| socle | C2×C3 | C2×#4179 |
| hypercenter | C22 | #6878⋊C2 |
| hypocenter | C92 | C3×D4 |
| LCS | G ▷ C2×C92 ▷ C92 | |
| UCS | C1 ◁ C2 ◁ C22 | |
143 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 143 conjugacy classes of subgroups — too many to draw. Only its 27 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|e^3=g,f^3=h,b^a=bd,e^a=e^2g^2,f^a=f^2h^2,g^a=g^2,h^a=h^2,e^c=ef,f^c=fg^2,g^c=gh79 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 473);