Finite Group DatabasebetaFinite Group Databasebeta| order | 10126 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×D61 |
| unambiguous semidirect product | C61⋊(C2×C83) |
| Fitting, socle, Hall | C61×C83 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C83 |
| Frattini | C1 | G |
| Fitting, socle | C61×C83 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C83 | |
8 conjugacy classes of subgroups.
2656 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C83×#6923, C83⋊#6923, D61×D83, … |
| maximal normal subgroup of | C83×#6923, C83⋊#6923, D61×D83, … |
| maximal quotient of | C83×Dic61, C2×C83×D61, C3×C83×D61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10126, 1);