Finite Group DatabasebetaFinite Group Databasebeta| order | 7514 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D13×C289 |
| unambiguous semidirect product | C13⋊(C2×C289) |
| Fitting, Hall | C13×C289 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D13 |
| commutator, hypocenter | C13 | C2×C289 |
| Frattini | C17 | C17×D13 |
| Fitting | C13×C289 | C2 |
| socle | C13×C17 | C2×C17 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C289 | |
12 conjugacy classes of subgroups.
2312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #261×C289, #28418609, D13×D289, … |
| maximal normal subgroup of | #261×C289, #28418609, D13×D289, … |
| maximal quotient of | Dic13×C289, C2×D13×C289, C3×D13×C289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7514, 2);