Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×AGL(1,𝔽5)×C29⋊C7 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C29)⋊C72 |
| unambiguous semidirect product | (C7×AGL(1,𝔽5)×C29)⋊C7 |
| Fitting, socle | C5×C7×C29 ⋊ C4×C7 |
| derived, Hall | C5×C29 ⋊ C4×C72 |
| Hall | C5×C7×C29⋊C7 ⋊ C4 |
| Hall | AGL(1,𝔽5)×C29 ⋊ C72 |
| Sylow | C29 ⋊ C72×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C7×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | AGL(1,𝔽5)×C29⋊C7 |
| commutator, hypocenter | C5×C29 | C4×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C29 | C4×C7 |
| prime radical | C7×D5×C29⋊C7 | C2 |
| cosocle | D5×C29 | C2×C72 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C7 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1015 |
385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 78);