Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #17984639⋊C2 |
| unambiguous semidirect product | #17984641⋊C2 |
| unambiguous semidirect product | #17984645⋊C2 |
| Fitting, socle, derived, Hall | C13×C19 ⋊ C22×C9 |
| Hall | #14555740 ⋊ C22 |
| Hall | D13×D19 ⋊ C9 |
| Sylow | C19 ⋊ C2×D13⋊C9 |
| Sylow | C13 ⋊ C2×AGL(1,𝔽19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C19 | C22×C9 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,13,19|c^3=d,f^a=f^18,e^b=e^12,e^c=e^3,f^c=f^16,f^d=f^1156 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×AGL(1,𝔽19), #72277847 |
| maximal normal subgroup of | D13⋊C3×AGL(1,𝔽19), #72277847 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 145);