Finite Group DatabasebetaFinite Group Databasebeta| order | 2940 |
| isoclinism | isoclinic class of C3⋊(C7⋊AGL(1,𝔽5)) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊(C7⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C3⋊(C7×C7⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C7⋊(C7×ΓL(1,𝔽16)) |
| Fitting, socle, Hall | C3×C5×C72 ⋊ C4 |
| derived | C3×C5×C7 ⋊ C4×C7 |
| Hall | C5×C72 ⋊ Dic3 |
| Hall | C3×C72 ⋊ AGL(1,𝔽5) |
| Sylow | C72 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ C7×Dic7 |
| Sylow | C5 ⋊ C7×Dic21 |
| Sylow | C3 ⋊ C7×C7⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C7⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C3×C5×C7 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72 | C4 |
| prime radical | C3×C72×D5 | C2 |
| cosocle | C3×C7×D5 | C2×C7 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C7 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2940, 150);