Finite Group DatabasebetaFinite Group Databasebeta| order | 5084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×D41 |
| unambiguous semidirect product | (C41×D31)⋊C2 |
| unambiguous semidirect product | (C31×D41)⋊C2 |
| unambiguous semidirect product | D1271⋊C2 |
| Fitting, socle, derived, Hall | C31×C41 ⋊ C22 |
| Sylow | C41 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C41 | C22 |
| LCS | G ▷ C31×C41 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
374 conjugacy classes — view the full character table.
| maximal subgroup of | D41×D31⋊C3, C3×D31×D41, D41×D93, … |
| maximal normal subgroup of | D41×D31⋊C3, C3×D31×D41, #27163260⋊C2, … |
| maximal quotient of | C3×D31×D41, D41×D93, D31×D123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5084, 8);