Finite Group DatabasebetaFinite Group Databasebeta| order | 18502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | C11⋊(C29⋊D29) |
| unambiguous semidirect product | C29⋊D319 |
| Fitting, socle, derived, Hall | C11×C292 ⋊ C2 |
| Sylow | C292 ⋊ D11 |
| Sylow | C11 ⋊ C29⋊D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C292 | C2 |
| LCS | G ▷ C11×C292 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9251 |
Polycyclic presentation:
2,11,29^2|b^a=b^10,c^a=c^28,d^a=d^284627 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×D319, D11×C29⋊D29, C2×C11⋊(C29⋊D29) |
| maximal normal subgroup of | D29×D319, D11×C29⋊D29, C2×C11⋊(C29⋊D29) |
| maximal quotient of | C11⋊#16809854, C2×C11⋊(C29⋊D29) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18502, 6);