Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊#226 |
| Sylow | C41 ⋊ #226 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4⋊D41 |
| commutator, prime radical, cosocle, hypocenter | SL(2,𝔽3)×C41 | C2 |
| Fitting | Q8×C41 | D3 |
| socle | C2×C41 | S4 |
| LCS | G ▷ SL(2,𝔽3)×C41 | |
| UCS | C1 ◁ C2 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2,3,41,2^3|a^2=f,d^2=f,e^2=f,b^a=b^2,c^a=c^40,d^a=de,e^a=ef,d^b=e,e^b=def,e^d=ef148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 101);