Finite Group DatabasebetaFinite Group Databasebeta| order | 14812 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C529 · Schur multiplier (H2) = C2 |
| direct product | C2×D7×C529 |
| unambiguous semidirect product | C7⋊(C22×C529) |
| unambiguous semidirect product | (C2×C7)⋊(C2×C529) |
| Fitting | C2×C7×C529 ⋊ C2 |
| derived, Sylow | C7 ⋊ C22×C529 |
| Hall | C7×C529 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C529 | D7 |
| commutator, hypocenter | C7 | C22×C529 |
| Frattini | C23 | C2×D7×C23 |
| Fitting | C2×C7×C529 | C2 |
| socle | C2×C7×C23 | C2×C23 |
| prime radical | C2×D7×C23 | C23 |
| cosocle | C7×C23 | C22×C23 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C529 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7406 |
5290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14812, 8);