Finite Group DatabasebetaFinite Group Databasebeta| order | 29820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C71⋊C7)⋊Dic5) |
| unambiguous semidirect product | (C71⋊C7)⋊Dic15 |
| unambiguous semidirect product | Dic1065⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C5⋊(D71⋊C7)) |
| commutator, hypocenter | C3×C5×C71 | C4×C7 |
| Fitting, socle, cosocle | C2×C3×C5×C71 | C2×C7 |
| prime radical | C2×C3×C5×C71⋊C7 | C2 |
| LCS | G ▷ C3×C5×C71 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4260 |
Polycyclic presentation:
2,3,5,7,71,2|a^2=f,b^a=b^2,c^a=c^4,e^a=e^70,e^d=e^45276 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29820, 28);