Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic3⋊#4223 |
| Hall | C3×C41 ⋊ C4⋊C4 |
| Sylow | C41 ⋊ Dic3⋊C4 |
| Sylow | C3 ⋊ C4⋊#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#4223 |
| commutator, Fitting, socle | C2×C3×C41 | C2×C4 |
| prime radical, cosocle | C2×C3×D41 | C22 |
| hypocenter | C3×C41 | C4⋊C4 |
| LCS | G ▷ C2×C3×C41 ▷ C3×C41 | |
| UCS | C1 ◁ C2 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 492 |
Polycyclic presentation:
2^4,3,41|a^2=c,b^2=d,b^a=bd,f^a=f^32,e^b=e^2,f^c=f^4078 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 93);