Finite Group DatabasebetaFinite Group Databasebeta| order | 19700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C25×C197 ⋊ C4 |
| Sylow | C197 ⋊ Dic25 |
| Sylow | C25 ⋊ #11716161 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C197 | C4 |
| Frattini | C5 | #16841102 |
| socle | C5×C197 | Dic5 |
| prime radical | C5×D197 | D5 |
| cosocle | C25×D197 | C2 |
| LCS | G ▷ C25×C197 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4925 |
Polycyclic presentation:
2^2,5,197,5|a^2=b,c^5=e^4,c^a=c^4e,d^a=d^183,e^a=e^4,d^b=d^1961253 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19700, 11);