Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C49 · Schur multiplier (H2) = C2 |
| direct product | C5×C49×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C5×C49 | A5 |
| commutator, hypocenter | A5 | C5×C49 |
| Frattini, cosocle | C7 | C5×C7×A5 |
| socle, prime radical | C5×C7×A5 | C7 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C5×C49 | |
60 conjugacy classes of subgroups.
1225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 770);