Finite Group DatabasebetaFinite Group Databasebeta| order | 29820 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊Dic355 |
| unambiguous semidirect product | C71⋊(ΓL(1,𝔽8)⋊Dic5) |
| unambiguous semidirect product | Dic2485⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(ΓL(1,𝔽8)⋊D71) |
| commutator, hypocenter | C5×C7×C71 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C7×C71 | C2×C3 |
| prime radical | C2×C5×ΓL(1,𝔽8)×C71 | C2 |
| LCS | G ▷ C5×C7×C71 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9940 |
Polycyclic presentation:
2,3,5,7,71,2|a^2=f,c^a=c^4,d^a=d^6,e^a=e^70,d^b=d^21784 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29820, 45);