Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D17×D25 |
| unambiguous semidirect product | (C17×D25)⋊(C2×C3) |
| unambiguous semidirect product | (C25×D17)⋊(C2×C3) |
| unambiguous semidirect product | D425⋊(C2×C3) |
| Fitting, Hall | C3×C17×C25 ⋊ C22 |
| derived, Hall | C17×C25 ⋊ C22×C3 |
| Hall | C3×C25 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C2×C3×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D17×D25 |
| commutator, hypocenter | C17×C25 | C22×C3 |
| Frattini | C5 | C3×D5×D17 |
| Fitting | C3×C17×C25 | C22 |
| socle | C3×C5×C17 | C2×D5 |
| LCS | G ▷ C17×C25 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
420 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D17×D25, C32×D17×D25, C3×D17×D75, … |
| maximal normal subgroup of | C9×D17×D25, C32×D17×D25, C3×C7×D17×D25 |
| maximal quotient of | C9×D17×D25, C32×D17×D25, C3×D17×D75, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 22);