Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C3⋊(C11⋊#261) |
| unambiguous semidirect product | C3⋊(C11×C11⋊#261) |
| unambiguous semidirect product | C11⋊(C11×C3⋊#261) |
| Fitting, socle, Hall | C3×C112×C13 ⋊ C4 |
| derived | C3×C11×C13 ⋊ C4×C11 |
| Hall | C112×C13 ⋊ Dic3 |
| Hall | C3×C112 ⋊ #261 |
| Sylow | C112 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ C11×Dic11 |
| Sylow | C13 ⋊ C11×Dic33 |
| Sylow | C3 ⋊ C11×C11⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(C11⋊#261) |
| commutator, hypocenter | C3×C11×C13 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C13 | C4 |
| prime radical | C3×C112×D13 | C2 |
| cosocle | C3×C11×D13 | C2×C11 |
| LCS | G ▷ C3×C11×C13 | |
| UCS | C1 ◁ C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 858 |
1485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 128);