Finite Group DatabasebetaFinite Group Databasebeta| order | 20300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15668505⋊C7 |
| Fitting, derived, Hall | C25×C29 ⋊ C4×C7 |
| Hall | C25×C29⋊C7 ⋊ C4 |
| Hall | #15668505 ⋊ C7 |
| Hall | C29⋊C7 ⋊ Dic25 |
| Sylow | C29 ⋊ C7×Dic25 |
| Sylow | C25 ⋊ AGL(1,𝔽29) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C29 | C4×C7 |
| Frattini | C5 | #10596817⋊C7 |
| socle | C5×C29 | C7×Dic5 |
| prime radical | C5×D29⋊C7 | D5 |
| cosocle | C25×D29 | C2×C7 |
| LCS | G ▷ C25×C29 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 725 |
Polycyclic presentation:
2,7,2,5,29,5|a^2=c,d^5=f^4,d^a=d^4f,e^a=e^17,f^a=f^4,e^b=e^16,e^c=e^28221 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20300, 19);