Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×D51 |
| unambiguous semidirect product | (C3×D5)⋊(C5×D17) |
| unambiguous semidirect product | (D5×C17)⋊(C5×D3) |
| Fitting, socle, Hall | C3×C52×C17 ⋊ C22 |
| derived | C3×C5×C17 ⋊ C22×C5 |
| Hall | C52×C17 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D51 |
| Sylow | C17 ⋊ C5×D3×D5 |
| Sylow | C3 ⋊ C5×D5×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×D51 |
| commutator, hypocenter | C3×C5×C17 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C17 | C22 |
| LCS | G ▷ C3×C5×C17 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
540 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D5×D153, D51×#3874, C3×C5×D5×D51, … |
| maximal normal subgroup of | C3×C5×D5×D51, C5×C7×D5×D51 |
| maximal quotient of | C5×D5×D153, C3×C5×D5×D51, C5×D5×C3⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 108);