Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×AGL(1,𝔽13) |
| unambiguous semidirect product | #261⋊(C3×C112) |
| unambiguous semidirect product | (C11×#261)⋊(C3×C11) |
| Fitting, socle, Hall | C112×C13 ⋊ C3×C4 |
| derived, Sylow | C13 ⋊ C3×C4×C112 |
| Hall | C112×#261 ⋊ C3 |
| Hall | C112×C13⋊C3 ⋊ C4 |
| Hall | #261 ⋊ C3×C112 |
| Hall | C13⋊C3 ⋊ C4×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C3×C4×C112 |
| Frattini | C1 | G |
| Fitting, socle | C112×C13 | C3×C4 |
| prime radical | C112×D13⋊C3 | C2 |
| cosocle | D13 | C2×C3×C112 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C112 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
1573 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 70);