Finite Group DatabasebetaFinite Group Databasebeta| order | 2100 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×ΓL(1,𝔽16) |
| unambiguous semidirect product | C3⋊(C5×C7×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C3×C52×C7 ⋊ C4 |
| derived | C3×C5 ⋊ C4×C5×C7 |
| Hall | C52×C7 ⋊ Dic3 |
| Hall | C3×C52 ⋊ C4×C7 |
| Sylow | C52 ⋊ C7×Dic3 |
| Hall | C3×C7 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C3 ⋊ C5×C7×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C4×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C4 |
| prime radical | C3×C5×C7×D5 | C2 |
| cosocle | C3×D5 | C2×C5×C7 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C5×C7 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 420 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2100, 122);