Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D5×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×D5×D11 |
| unambiguous semidirect product | (D5×C11)⋊(C22×C3) |
| unambiguous semidirect product | (C5×D11)⋊(C22×C3) |
| unambiguous semidirect product | D55⋊(C22×C3) |
| Fitting, socle | C2×C3×C5×C11 ⋊ C22 |
| derived, Hall | C5×C11 ⋊ C23×C3 |
| Hall | C3×C5×C11 ⋊ C23 |
| Hall | C3×C11 ⋊ C22×D5 |
| Hall | C3×C5 ⋊ C22×D11 |
| Sylow | C11 ⋊ C22×C3×D5 |
| Sylow | C5 ⋊ C22×C3×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D5×D11 |
| commutator, cosocle, hypocenter | C5×C11 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C11 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C2×C3 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 166);