Finite Group DatabasebetaFinite Group Databasebeta| order | 29820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C3⋊(C7⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C3⋊(C71×C7⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C7⋊(ΓL(1,𝔽16)×C71) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C3⋊(C7⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C3×C5×C7 | C4×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C71 | C4 |
| prime radical | C3×C7×D5×C71 | C2 |
| cosocle | C3×C7×D5 | C2×C71 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C71 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7455 |
3195 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29820, 135);