Finite Group DatabasebetaFinite Group Databasebeta| order | 19900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic199 |
| unambiguous semidirect product | C199⋊(C4×C25) |
| derived, Sylow | C199 ⋊ C4×C25 |
| Hall | C25×C199 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D199 |
| commutator, hypocenter | C199 | C4×C25 |
| Frattini | C2×C5 | C5×D199 |
| Fitting | C2×C25×C199 | C2 |
| socle, prime radical, cosocle | C2×C5×C199 | C2×C5 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C2×C25 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19900 |
5050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19900, 3);