Finite Group DatabasebetaFinite Group Databasebeta| order | 7740 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C3 |
| direct product | C43×C3⋊ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(C43×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C32×C5×C43 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C43 |
| Hall | C32×C43 ⋊ AGL(1,𝔽5) |
| Hall | C5×C43 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ AGL(1,𝔽5)×C43 |
| Sylow | C5 ⋊ C3⋊Dic3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C3⋊ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C4×C43 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C43 | C4 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C43 | |
72 conjugacy classes of subgroups.
903 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7740, 93);