Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D29×D49 |
| unambiguous semidirect product | (C29×D49)⋊(C2×C5) |
| unambiguous semidirect product | (C49×D29)⋊(C2×C5) |
| unambiguous semidirect product | D1421⋊(C2×C5) |
| Fitting, Hall | C5×C29×C49 ⋊ C22 |
| derived, Hall | C29×C49 ⋊ C22×C5 |
| Hall | C5×C49 ⋊ C2×D29 |
| Hall | C5×C29 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×C5×D29 |
| Sylow | C29 ⋊ C2×C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D29×D49 |
| commutator, cosocle, hypocenter | C29×C49 | C22×C5 |
| Frattini | C7 | C5×D7×D29 |
| Fitting | C5×C29×C49 | C22 |
| socle | C5×C7×C29 | C2×D7 |
| LCS | G ▷ C29×C49 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7105 |
2080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 27);