Finite Group DatabasebetaFinite Group Databasebeta| order | 21538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C121 · Schur multiplier (H2) = C1 |
| direct product | C2×C89⋊C121 |
| unambiguous semidirect product | (C2×C89)⋊C121 |
| derived, Sylow | C89 ⋊ C2×C121 |
| Hall | C2×C89 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | C89⋊C11 |
| commutator, hypocenter | C89 | C2×C121 |
| Frattini | C11 | C2×C89⋊C11 |
| Fitting, socle, prime radical | C2×C11×C89 | C11 |
| cosocle | C11×C89 | C2×C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21538 |
418 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21538, 3);