Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(#10596815⋊C7) |
| unambiguous semidirect product | (C7⋊#10596815)⋊C7 |
| Fitting, socle, derived | C5×C7×C29 ⋊ C4×C7 |
| Hall | C5×C7×C29⋊C7 ⋊ C4 |
| Hall | C7×C29⋊C7 ⋊ AGL(1,𝔽5) |
| Hall | C5×C29 ⋊ C7×Dic7 |
| Sylow | C29 ⋊ C7×C7⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C7⋊AGL(1,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C29 | C4×C7 |
| prime radical | C7×C5⋊(D29⋊C7) | C2 |
| cosocle | C7×D145 | C2×C7 |
| LCS | G ▷ C5×C7×C29 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1015 |
Polycyclic presentation:
2,7,2,5,7,29|a^2=c,d^a=d^2,e^a=e^6,f^a=f^12,f^b=f^16,d^c=d^4,f^c=f^28154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 80);