Finite Group DatabasebetaFinite Group Databasebeta| order | 12780 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C71 · Schur multiplier (H2) = C2 |
| direct product | C3×A5×C71 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C71 | A5 |
| commutator, hypocenter | A5 | C3×C71 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C3×C71 | |
42 conjugacy classes of subgroups.
1065 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12780, 119);