Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D35⋊D29 |
| unambiguous semidirect product | D35⋊(C7×D29) |
| Fitting, socle, Hall | C5×C72×C29 ⋊ C22 |
| derived | C5×C7×C29 ⋊ C22×C7 |
| Hall | C72×C29 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D29 |
| Hall | C5×C29 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ D5×D29 |
| Sylow | C29 ⋊ C7×D5×D7 |
| Sylow | C5 ⋊ C7×D7×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D35⋊D29 |
| commutator, cosocle, hypocenter | C5×C7×C29 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C29 | C22 |
| LCS | G ▷ C5×C7×C29 | |
| UCS | C1 ◁ C7 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2030 |
2002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 136);