Finite Group DatabasebetaFinite Group Databasebeta| order | 15664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽89) |
| Fitting, socle | C2×C89 ⋊ C8×C11 |
| derived, Sylow | C89 ⋊ C2×C8×C11 |
| Hall | C2×#10623505 ⋊ C11 |
| Hall | C89⋊C11 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽89) |
| commutator, hypocenter | C89 | C2×C8×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C89 | C8×C11 |
| prime radical | C2×D89⋊C11 | C4 |
| cosocle | #67063 | C22×C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 178 |
178 conjugacy classes — view the full character table.
| holomorph of | C2×C89 |
Past the SmallGroups library coverage — no SmallGroups id.