Finite Group DatabasebetaFinite Group Databasebeta| order | 10706 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×D101 |
| unambiguous semidirect product | C101⋊(C2×C53) |
| Fitting, socle, Hall | C53×C101 ⋊ C2 |
| derived, Sylow | C101 ⋊ C2×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D101 |
| commutator, cosocle, hypocenter | C101 | C2×C53 |
| Frattini | C1 | G |
| Fitting, socle | C53×C101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C53 | |
8 conjugacy classes of subgroups.
2756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#87938, #36339129, D53×D101, … |
| maximal normal subgroup of | C53×#87938, #36339129, D53×D101, … |
| maximal quotient of | C53×Dic101, C2×C53×D101, C3×C53×D101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10706, 2);