Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C112×#261) |
| Fitting, socle, Hall | C3×C112×C13 ⋊ C4 |
| derived, Hall | C3×C13 ⋊ C4×C112 |
| Hall | C112×C13 ⋊ Dic3 |
| Hall | C3×C112 ⋊ #261 |
| Sylow | C13 ⋊ C112×Dic3 |
| Sylow | C3 ⋊ C112×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C4×C112 |
| Frattini | C1 | G |
| Fitting, socle | C3×C112×C13 | C4 |
| prime radical | C3×C112×D13 | C2 |
| cosocle | C3×D13 | C2×C112 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C112 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4719 |
1815 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 126);