Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C310 |
| unambiguous semidirect product | C4⋊(C3⋊(C3⋊(C3⋊(C3⋊D3)))) |
| Fitting | C35×C4 ⋊ C2 |
| Sylow | C35 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C3⋊(C3⋊(C3⋊(C3⋊D3))) |
| commutator, socle, cosocle | C2×C35 | C22 |
| Fitting | C35×C4 | C2 |
| hypercenter | C4 | C3⋊(C3⋊(C3⋊(C3⋊D3))) |
| hypocenter | C35 | D4 |
| LCS | G ▷ C2×C35 ▷ C35 | |
| UCS | C1 ◁ C2 ◁ C4 | |
21312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 972 |
Polycyclic presentation:
2^3,3^5|b^2=c,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^2,h^a=h^2489 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3868);