Finite Group DatabasebetaFinite Group Databasebeta| order | 21538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊D979 |
| unambiguous semidirect product | C89⋊(C11⋊D11) |
| Fitting, socle, derived, Hall | C112×C89 ⋊ C2 |
| Sylow | C112 ⋊ D89 |
| Sylow | C89 ⋊ C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C89 | C2 |
| LCS | G ▷ C112×C89 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10769 |
Polycyclic presentation:
2,11^2,89|b^a=b^10,c^a=c^10,d^a=d^885386 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21538, 16);