Finite Group DatabasebetaFinite Group Databasebeta| order | 10486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D749 |
| unambiguous semidirect product | C7⋊(C7×D107) |
| unambiguous semidirect product | C107⋊(C7×D7) |
| Fitting, socle, Hall | C72×C107 ⋊ C2 |
| derived | C7×C107 ⋊ C2×C7 |
| Sylow | C107 ⋊ C7×D7 |
| Sylow | C72 ⋊ D107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D749 |
| commutator, cosocle, hypocenter | C7×C107 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C107 | C2 |
| LCS | G ▷ C7×C107 | |
| UCS | C1 ◁ C7 | |
22 conjugacy classes of subgroups.
2632 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D107, D7×D749, (C7⋊D7)⋊D107, … |
| maximal normal subgroup of | C7×D7×D107, D7×D749, (C7⋊D7)⋊D107, … |
| maximal quotient of | C7×Dic749, C2×C7×D749, C3×C7×D749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10486, 8);