Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×C49×D53 |
| unambiguous semidirect product | C53⋊(C22×C49) |
| unambiguous semidirect product | (C2×C53)⋊(C2×C49) |
| Fitting | C2×C49×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C22×C49 |
| Hall | C49×C53 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D53 |
| commutator, hypocenter | C53 | C22×C49 |
| Frattini | C7 | C2×C7×D53 |
| Fitting | C2×C49×C53 | C2 |
| socle | C2×C7×C53 | C2×C7 |
| prime radical | C2×C7×D53 | C7 |
| cosocle | C7×C53 | C22×C7 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C49 | |
30 conjugacy classes of subgroups.
2744 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D53×C49⋊C3, D3×C49×D53, C2×C3×C49×D53, … |
| maximal normal subgroup of | C2×D53×C49⋊C3, C2×C3×C49×D53 |
| maximal quotient of | D3×C49×D53, C2×C3×C49×D53, C2×C49×D159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 9);