Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4296⋊#261 |
| Fitting, socle, derived, Hall | C13×C19 ⋊ C4×C9 |
| Hall | C13×#4296 ⋊ C4 |
| Hall | C19⋊#261 ⋊ C9 |
| Hall | #4296 ⋊ #261 |
| Sylow | C19 ⋊ C9×#261 |
| Sylow | C13 ⋊ #4296⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C19 | C4×C9 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,13,19|a^2=c,b^3=d,e^a=e^5,f^a=f^18,f^b=f^4,e^c=e^12,f^d=f^771 conjugacy classes — view the full character table.
| maximal subgroup of | #261×AGL(1,𝔽19), #72277791 |
| maximal normal subgroup of | #261×AGL(1,𝔽19), #72277791 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 147);