Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | D7×C29×D35 |
| unambiguous semidirect product | (C5×D7)⋊(D7×C29) |
| unambiguous semidirect product | (C7×D7)⋊(D5×C29) |
| Fitting, socle, Hall | C5×C72×C29 ⋊ C22 |
| derived, Hall | C5×C72 ⋊ C22×C29 |
| Hall | C72×C29 ⋊ C2×D5 |
| Hall | C5×C29 ⋊ D72 |
| Sylow | C72 ⋊ C2×D5×C29 |
| Sylow | C5 ⋊ D72×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D7×D35 |
| commutator, cosocle, hypocenter | C5×C72 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C29 | C22 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C29 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2030 |
2755 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 137);