Finite Group DatabasebetaFinite Group Databasebeta| order | 21538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C11×D89⋊C11 |
| unambiguous semidirect product | D89⋊C112 |
| unambiguous semidirect product | (C89⋊C11)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D89)⋊C11 |
| Fitting, socle | C11×C89 ⋊ C2×C11 |
| derived, Sylow | C89 ⋊ C2×C112 |
| Hall | C11×C89⋊C11 ⋊ C2 |
| Hall | D89 ⋊ C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D89⋊C11 |
| commutator, cosocle, hypocenter | C89 | C2×C112 |
| Frattini | C1 | G |
| Fitting, socle | C11×C89 | C2×C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 979 |
286 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21538, 8);