Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7⋊AGL(1,𝔽5)×C29⋊C7 |
| unambiguous semidirect product | C7⋊(AGL(1,𝔽5)×C29⋊C7) |
| unambiguous semidirect product | (C29×C7⋊AGL(1,𝔽5))⋊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 ⋊ Dic7×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C29 | C4×C7 |
| prime radical | C7×D5×C29⋊C7 | C2 |
| cosocle | C7×D5×C29 | C2×C7 |
| LCS | G ▷ C5×C7×C29 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1015 |
187 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 82);