Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C19 ⋊ C32×C4 |
| Hall | C13⋊C3×C19⋊C3 ⋊ C4 |
| Hall | C19×#261 ⋊ C32 |
| Hall | #261 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×C4×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C19 | C32×C4 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
117 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×#4296, D19⋊C3×AGL(1,𝔽13) |
| maximal normal subgroup of | AGL(1,𝔽13)×#4296, D19⋊C3×AGL(1,𝔽13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 143);