Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | #261⋊(C112⋊C3) |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C3×C4 |
| Hall | C112×#261 ⋊ C3 |
| Hall | C13⋊(C112⋊C3) ⋊ C4 |
| Sylow | C112 ⋊ AGL(1,𝔽13) |
| Hall | #261 ⋊ C112⋊C3 |
| Sylow | C13 ⋊ C4×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C13 | C3×C4 |
| prime radical | D13⋊(C112⋊C3) | C2 |
| cosocle | C112×D13 | C2×C3 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 429 |
Polycyclic presentation:
2,3,2,11^2,13|a^2=c,f^a=f^5,d^b=d^3e^9,e^b=de^7,f^b=f^3,f^c=f^12293 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 100);