Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic425 |
| derived, Hall | C17×C25 ⋊ C3×C4 |
| Hall | C3×C17×C25 ⋊ C4 |
| Hall | C3×C25 ⋊ Dic17 |
| Hall | C3×C17 ⋊ Dic25 |
| Sylow | C25 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ C3×Dic25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D425 |
| commutator, hypocenter | C17×C25 | C3×C4 |
| Frattini | C2×C5 | C3×D85 |
| Fitting | C2×C3×C17×C25 | C2 |
| socle | C2×C3×C5×C17 | D5 |
| LCS | G ▷ C17×C25 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
1284 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic425, C32×Dic425, C3×Dic1275, … |
| maximal normal subgroup of | C9×Dic425, C32×Dic425, C3×C7×Dic425 |
| maximal quotient of | C9×Dic425, C32×Dic425, C3×Dic1275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 4);