Finite Group DatabasebetaFinite Group Databasebeta| order | 10540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic155 |
| unambiguous semidirect product | C31⋊(C17×Dic5) |
| derived, Hall | C5×C31 ⋊ C4×C17 |
| Hall | C5×C17×C31 ⋊ C4 |
| Hall | C17×C31 ⋊ Dic5 |
| Hall | C5×C17 ⋊ Dic31 |
| Sylow | C31 ⋊ C17×Dic5 |
| Sylow | C5 ⋊ C17×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D155 |
| commutator, hypocenter | C5×C31 | C4×C17 |
| Frattini | C2 | C17×D155 |
| Fitting, socle, prime radical | C2×C5×C17×C31 | C2 |
| cosocle | C2×C5×C31 | C2×C17 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C2×C17 | |
24 conjugacy classes of subgroups.
2686 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×Dic155, C17×Dic465, C17×(C31⋊C3)⋊Dic5 |
| maximal normal subgroup of | C3×C17×Dic155, C17×(C31⋊C3)⋊Dic5 |
| maximal quotient of | C3×C17×Dic155, C17×Dic465 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10540, 7);