Finite Group DatabasebetaFinite Group Databasebeta| order | 20300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×#10596816⋊C7 |
| unambiguous semidirect product | #10596816⋊(C5×C7) |
| unambiguous semidirect product | (C5×#10596816)⋊C7 |
| Fitting, socle, Hall | C52×C29 ⋊ C4×C7 |
| derived | C5×C29 ⋊ C4×C5×C7 |
| Hall | C52×C29⋊C7 ⋊ C4 |
| Hall | C5×#10596816 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C29 ⋊ C5×C7×AGL(1,𝔽5) |
| Sylow | C52 ⋊ Dic29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #10596816⋊C7 |
| commutator, hypocenter | C5×C29 | C4×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C29 | C4×C7 |
| prime radical | C5×D5×C29⋊C7 | C2 |
| cosocle | D5×C29 | C2×C5×C7 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 580 |
215 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20300, 75);