Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D1015 |
| unambiguous semidirect product | (C5×D7)⋊D203 |
| unambiguous semidirect product | (C7×D7)⋊D145 |
| unambiguous semidirect product | (D7×C29)⋊D35 |
| Fitting, socle, derived, Hall | C5×C72×C29 ⋊ C22 |
| Hall | C72×C29 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D29 |
| Hall | C5×C29 ⋊ D72 |
| Sylow | C72 ⋊ C2×D145 |
| Sylow | C29 ⋊ D7×D35 |
| Sylow | C5 ⋊ D7×D203 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C29 | C22 |
| LCS | G ▷ C5×C72×C29 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2030 |
2545 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 138);