Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| direct product | C3×C11⋊(C11⋊#261) |
| unambiguous semidirect product | C11⋊(C3×C11⋊#261) |
| Fitting, socle, Hall | C3×C112×C13 ⋊ C4 |
| derived, Hall | C112×C13 ⋊ C3×C4 |
| Hall | C3×C112 ⋊ #261 |
| Sylow | C112 ⋊ C3×#261 |
| Hall | C3×C13 ⋊ C11⋊Dic11 |
| Sylow | C13 ⋊ C3×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊(C11⋊#261) |
| commutator, hypocenter | C112×C13 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C13 | C4 |
| prime radical | C3×C112×D13 | C2 |
| cosocle | C112×D13 | C2×C3 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 ◁ C3 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4719 |
1461 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 118);