Finite Group DatabasebetaFinite Group Databasebeta| order | 19700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊D197 |
| unambiguous semidirect product | D985⋊D5 |
| Fitting, socle, derived, Hall | C52×C197 ⋊ C22 |
| Sylow | C197 ⋊ D52 |
| Sylow | C52 ⋊ C2×D197 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C197 | C22 |
| LCS | G ▷ C52×C197 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1970 |
Polycyclic presentation:
2^2,5^2,197|c^a=c^4,e^a=e^196,c^b=c^4,d^b=d^41388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19700, 45);