Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | C5⋊D5×D51 |
| Fitting, socle, derived, Hall | C3×C52×C17 ⋊ C22 |
| Hall | C52×C17 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D51 |
| Sylow | C17 ⋊ D3×C5⋊D5 |
| Sylow | C3 ⋊ D17×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C17 | C22 |
| LCS | G ▷ C3×C52×C17 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
378 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×D153, D51×(C5⋊D5)⋊C3, C3×C5⋊D5×D51, … |
| maximal normal subgroup of | D51×(C5⋊D5)⋊C3, C3×C5⋊D5×D51, C7×C5⋊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, 125);