Finite Group DatabasebetaFinite Group Databasebeta| order | 19775 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C113⋊C7 |
| unambiguous semidirect product | C113⋊(C7×C25) |
| unambiguous semidirect product | (C25×C113)⋊C7 |
| Fitting, Hall | C25×C113 ⋊ C7 |
| derived, Sylow | C113 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C113⋊C7 |
| commutator, hypocenter | C113 | C7×C25 |
| Frattini | C5 | C5×C113⋊C7 |
| Fitting | C25×C113 | C7 |
| socle, cosocle | C5×C113 | C5×C7 |
| prime radical | C5×C113⋊C7 | C5 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2825 |
575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19775, 2);