Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic145⋊C49 |
| derived, Hall | C5×C29 ⋊ C4×C49 |
| Hall | C5×C29⋊C49 ⋊ C4 |
| Hall | C29⋊C49 ⋊ Dic5 |
| Hall | Dic145 ⋊ C49 |
| Sylow | C29 ⋊ Dic5×C49 |
| Sylow | C5 ⋊ Dic29⋊C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C7 | C5⋊(D29⋊C7) |
| commutator, hypocenter | C5×C29 | C4×C49 |
| Fitting, socle, prime radical, cosocle | C2×C5×C7×C29 | C2×C7 |
| LCS | G ▷ C5×C29 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28420 |
Polycyclic presentation:
2,5,7,29,2,7|a^2=e,c^7=f,b^a=b^4,d^a=d^28,d^c=d^16532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 12);