Finite Group DatabasebetaFinite Group Databasebeta| order | 21516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C11⋊(D163⋊C3) |
| unambiguous semidirect product | (C2×C11)⋊(D163⋊C3) |
| unambiguous semidirect product | (C2×C163⋊C3)⋊D11 |
| unambiguous semidirect product | (C2×D1793)⋊C3 |
| Fitting, socle | C2×C11×C163 ⋊ C2×C3 |
| derived, Hall | C11×C163 ⋊ C22×C3 |
| Hall | C2×D1793 ⋊ C3 |
| Hall | C11×C163⋊C3 ⋊ C22 |
| Hall | C163⋊C3 ⋊ C2×D11 |
| Sylow | C163 ⋊ C2×C3×D11 |
| Sylow | C11 ⋊ C2×D163⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C11⋊(D163⋊C3) |
| commutator, cosocle, hypocenter | C11×C163 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C163 | C2×C3 |
| LCS | G ▷ C11×C163 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3586 |
636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21516, 16);