Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C16 · Schur multiplier (H2) = C1 |
| direct product | C5×#2258⋊C3 |
| unambiguous semidirect product | #2258⋊(C3×C5) |
| unambiguous semidirect product | (C5×#2258)⋊C3 |
| Fitting, Hall | C5×#2258 ⋊ C3 |
| Sylow | #2258 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C32 | A4 |
| commutator, hypocenter | Q8 | C3×C5×C16 |
| Frattini | C16 | C2×C5×A4 |
| Fitting | C5×#2258 | C3 |
| socle | C2×C5 | A4×C16 |
| prime radical | C5×#41⋊C3 | C8 |
| cosocle | #504 | C2×C3×C5 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C5×C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236401);