Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C8×C3⋊#674 |
| derived, Hall | C3×C5 ⋊ C8×C16 |
| Sylow | C5 ⋊ C8×C3⋊C16 |
| Sylow | C3 ⋊ C8×#674 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C8×C16 |
| Frattini | C42 | C2×ΓL(1,𝔽16) |
| Fitting | C3×C4×C5×C8 | C4 |
| socle, prime radical | C22×C3×C5 | C4×C8 |
| cosocle | C3×C4×#168 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C4×C8 | |
208 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 3141);