Finite Group DatabasebetaFinite Group Databasebeta| order | 18850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C29 · Schur multiplier (H2) = C1 |
| direct product | C13×C29×D25 |
| unambiguous semidirect product | C25⋊(C2×C13×C29) |
| Fitting, Hall | C13×C25×C29 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C13×C29 |
| Hall | C25×C29 ⋊ C2×C13 |
| Hall | C13×C25 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C29 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C13×C29 |
| Frattini | C5 | D5×C13×C29 |
| Fitting | C13×C25×C29 | C2 |
| socle | C5×C13×C29 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C13×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9425 |
5278 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×C29×#1035, C13×#15668504, C29×#13049906, … |
| maximal normal subgroup of | C13×C29×#1035, C13×#15668504, C29×#13049906, … |
| maximal quotient of | C13×C29×Dic25, C2×C13×C29×D25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18850, 5);