Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C3⋊#66774 |
| unambiguous semidirect product | C3⋊(C5×#66774) |
| Fitting, socle, Hall | C3×C52×C17 ⋊ C4 |
| derived | C3×C5×C17 ⋊ C4×C5 |
| Hall | C52×C17 ⋊ Dic3 |
| Hall | C3×C52 ⋊ Dic17 |
| Hall | C3×C17 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ Dic51 |
| Sylow | C17 ⋊ C5×ΓL(1,𝔽16) |
| Sylow | C3 ⋊ C5×#66774 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#66774 |
| commutator, hypocenter | C3×C5×C17 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C4 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C5 | |
52 conjugacy classes of subgroups.
525 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9⋊#66774, C3×C5×C3⋊#66774, C5×C3⋊(C3⋊#66774), … |
| maximal normal subgroup of | C3×C5×C3⋊#66774, C5×C7×C3⋊#66774 |
| maximal quotient of | C5×C9⋊#66774, C3×C5×C3⋊#66774, C5×C3⋊(C3⋊#66774), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 104);