Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×Dic49 |
| unambiguous semidirect product | C49⋊(C4×C53) |
| derived, Sylow | C49 ⋊ C4×C53 |
| Hall | C49×C53 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D49 |
| commutator, hypocenter | C49 | C4×C53 |
| Frattini | C2×C7 | D7×C53 |
| Fitting | C2×C49×C53 | C2 |
| socle, prime radical | C2×C7×C53 | D7 |
| cosocle | C2×C49 | C2×C53 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C53 | |
18 conjugacy classes of subgroups.
2756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C53×Dic49, C53×Dic147, C53×(C49⋊C3)⋊C4 |
| maximal normal subgroup of | C3×C53×Dic49, C53×(C49⋊C3)⋊C4 |
| maximal quotient of | C3×C53×Dic49, C53×Dic147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 2);