Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×Dic51 |
| unambiguous semidirect product | C3⋊(C52×Dic17) |
| derived, Hall | C3×C17 ⋊ C4×C52 |
| Hall | C3×C52×C17 ⋊ C4 |
| Hall | C52×C17 ⋊ Dic3 |
| Hall | C3×C52 ⋊ Dic17 |
| Sylow | C17 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C52×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D51 |
| commutator, hypocenter | C3×C17 | C4×C52 |
| Frattini | C2 | C52×D51 |
| Fitting, socle | C2×C3×C52×C17 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C52 | |
96 conjugacy classes of subgroups.
1350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×Dic153, C52⋊C3×Dic51, C3×C52×Dic51, … |
| maximal normal subgroup of | C52⋊C3×Dic51, C3×C52×Dic51, C52×C7×Dic51 |
| maximal quotient of | C52×Dic153, C3×C52×Dic51, C52×C3⋊Dic51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 50);