Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C13 ⋊ C3×C4 |
| Hall | #20262573 ⋊ C3 |
| Hall | C112×C13⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ #92150 |
| Sylow | C13 ⋊ C3×#92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C13 | C3×C4 |
| prime radical | C11⋊(C11⋊(D13⋊C3)) | C2 |
| cosocle | C11⋊D143 | C2×C3 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
Polycyclic presentation:
2,3,2,11^2,13|a^2=c,d^a=d^5e^7,e^a=de^6,f^a=f^5,f^b=f^3,d^c=d^10,e^c=e^10,f^c=f^12223 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 97);