Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C29 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C29×D49 |
| unambiguous semidirect product | C49⋊(C22×C5×C29) |
| unambiguous semidirect product | (C2×C49)⋊(C2×C5×C29) |
| Fitting | C2×C5×C29×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C22×C5×C29 |
| Hall | C5×C29×C49 ⋊ C22 |
| Hall | C29×C49 ⋊ C22×C5 |
| Hall | C5×C49 ⋊ C22×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C29 | D49 |
| commutator, cosocle, hypocenter | C49 | C22×C5×C29 |
| Frattini | C7 | C2×C5×D7×C29 |
| Fitting | C2×C5×C29×C49 | C2 |
| socle | C2×C5×C7×C29 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C5×C29 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14210 |
7540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 49);