Finite Group DatabasebetaFinite Group Databasebeta| order | 14749 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C43×C49 ⋊ C7 |
| Sylow | C43 ⋊ 7−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C7 | C7×C43⋊C7 |
| commutator, socle, cosocle | C7×C43 | C72 |
| Fitting | C43×C49 | C7 |
| prime radical | C7×C43⋊C7 | C7 |
| hypercenter | C49 | C43⋊C7 |
| hypocenter | C43 | 7−1+2 |
| LCS | G ▷ C7×C43 ▷ C43 | |
| UCS | C1 ◁ C7 ◁ C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2107 |
Polycyclic presentation:
7^3,43|a^7=c,b^a=bc,d^b=d^16349 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14749, 13);