Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D11×A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
| direct product | D11×A5 |
| unambiguous semidirect product | C11⋊(C2×A5) |
| Fitting, Sylow | C11 ⋊ C2×A5 |
| socle, derived | C11×A5 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, socle, hypocenter | C11×A5 | C2 |
| Fitting, cosocle | C11 | C2×A5 |
| LCS | G ▷ C11×A5 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 55 |
35 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 137);