Finite Group DatabasebetaFinite Group Databasebeta| order | 18850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C29 · Schur multiplier (H2) = C5 |
| direct product | C13×C29×C5⋊D5 |
| unambiguous semidirect product | C5⋊(D5×C13×C29) |
| Fitting, socle, Hall | C52×C13×C29 ⋊ C2 |
| derived, Sylow | C52 ⋊ C2×C13×C29 |
| Hall | C52×C29 ⋊ C2×C13 |
| Hall | C52×C13 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C29 | C5⋊D5 |
| commutator, cosocle, hypocenter | C52 | C2×C13×C29 |
| Frattini | C1 | G |
| Fitting, socle | C52×C13×C29 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C13×C29 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9425 |
5278 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D52×C13×C29, C13×(C5⋊D5)⋊D29, C29×(C5⋊D5)⋊D13, … |
| maximal normal subgroup of | D52×C13×C29, C13×(C5⋊D5)⋊D29, C29×(C5⋊D5)⋊D13, … |
| maximal quotient of | C13×C29×#1039, C2×C13×C29×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18850, 13);