Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×#10596816 |
| Fitting, Hall | C5×C29×C49 ⋊ C4 |
| derived, Hall | C5×C29 ⋊ C4×C49 |
| Hall | C29×C49 ⋊ AGL(1,𝔽5) |
| Hall | C5×C49 ⋊ Dic29 |
| Sylow | C29 ⋊ AGL(1,𝔽5)×C49 |
| Sylow | C5 ⋊ C49×Dic29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #10596816 |
| commutator, hypocenter | C5×C29 | C4×C49 |
| Frattini | C7 | C7×#10596816 |
| Fitting | C5×C29×C49 | C4 |
| socle | C5×C7×C29 | C4×C7 |
| prime radical, cosocle | C7×D5×C29 | C2×C7 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C49 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7105 |
2989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 31);