Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10596814⋊C49 |
| derived, Hall | C5×C29 ⋊ C4×C49 |
| Hall | C5×C29⋊C49 ⋊ C4 |
| Hall | C29⋊C49 ⋊ AGL(1,𝔽5) |
| Hall | #10596814 ⋊ C49 |
| Sylow | C29 ⋊ AGL(1,𝔽5)×C49 |
| Sylow | C5 ⋊ #1181⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | #10596814⋊C7 |
| commutator, hypocenter | C5×C29 | C4×C49 |
| Fitting, socle | C5×C7×C29 | C4×C7 |
| prime radical, cosocle | C7×D145 | C2×C7 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7105 |
Polycyclic presentation:
2,7,2,5,29,7|a^2=c,b^7=f,d^a=d^2,e^a=e^17,e^b=e^16,d^c=d^4,e^c=e^28280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 15);