Finite Group DatabasebetaFinite Group Databasebeta| order | 5004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D139⋊C9 |
| unambiguous semidirect product | D139⋊(C2×C9) |
| unambiguous semidirect product | (C2×D139)⋊C9 |
| unambiguous semidirect product | (C139⋊C9)⋊C22 |
| unambiguous semidirect product | (C2×C139⋊C9)⋊C2 |
| derived, Sylow | C139 ⋊ C22×C9 |
| Hall | C139⋊C9 ⋊ C22 |
| Hall | C2×D139 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D139⋊C3 |
| commutator, hypocenter | C139 | C22×C9 |
| Frattini | C3 | C2×D139⋊C3 |
| Fitting, socle | C2×C3×C139 | C2×C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C3 | |
30 conjugacy classes of subgroups.
174 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D139⋊C9, C2×C5×D139⋊C9, C2×C5⋊(D139⋊C9), … |
| maximal normal subgroup of | C2×C5×D139⋊C9, C2×C7×D139⋊C9 |
| maximal quotient of | D5×D139⋊C9, C2×C5×D139⋊C9, C2×C5⋊(D139⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5004, 8);