Finite Group DatabasebetaFinite Group Databasebeta| order | 18502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C292 · Schur multiplier (H2) = C29 |
| direct product | D11×C292 |
| unambiguous semidirect product | C11⋊(C2×C292) |
| Fitting, socle, Hall | C11×C292 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C292 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C292 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C292 |
| Frattini | C1 | G |
| Fitting, socle | C11×C292 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C292 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9251 |
5887 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×C29×D29, D11×C29⋊D29, C2×D11×C292 |
| maximal normal subgroup of | D11×C29×D29, D11×C29⋊D29, C2×D11×C292 |
| maximal quotient of | C292×Dic11, C2×D11×C292 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18502, 8);