Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C11⋊AGL(1,𝔽13) |
| unambiguous semidirect product | C11⋊(C11×AGL(1,𝔽13)) |
| unambiguous semidirect product | (C11⋊#261)⋊(C3×C11) |
| unambiguous semidirect product | (C11×C11⋊#261)⋊C3 |
| Fitting, socle, Hall | C112×C13 ⋊ C3×C4 |
| derived | C11×C13 ⋊ C3×C4×C11 |
| Hall | C11×C11⋊#261 ⋊ C3 |
| Hall | C112×C13⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ C11×Dic11 |
| Sylow | C13 ⋊ C3×C11×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C11⋊AGL(1,𝔽13) |
| commutator, hypocenter | C11×C13 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C13 | C3×C4 |
| prime radical | C112×D13⋊C3 | C2 |
| cosocle | C11×D13 | C2×C3×C11 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
583 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 71);