Finite Group DatabasebetaFinite Group Databasebeta| order | 18850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C5×C29×D65 |
| unambiguous semidirect product | C5⋊(C5×D13×C29) |
| unambiguous semidirect product | C13⋊(C5×D5×C29) |
| Fitting, socle, Hall | C52×C13×C29 ⋊ C2 |
| derived | C5×C13 ⋊ C2×C5×C29 |
| Hall | C52×C29 ⋊ D13 |
| Hall | C13×C29 ⋊ C5×D5 |
| Hall | C52×C13 ⋊ C2×C29 |
| Sylow | C52 ⋊ D13×C29 |
| Sylow | C13 ⋊ C5×D5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C29 | D65 |
| commutator, cosocle, hypocenter | C5×C13 | C2×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C29 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C5×C29 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3770 |
4930 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D29×D65, C5×D5×D13×C29, C5×D65⋊D29, … |
| maximal normal subgroup of | C5×D29×D65, C5×D5×D13×C29, C5×D65⋊D29, … |
| maximal quotient of | C5×C29×Dic65, C2×C5×C29×D65 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18850, 15);