Finite Group DatabasebetaFinite Group Databasebeta| order | 1320 |
| isoclinism | isoclinic class of D3×C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic3×C11⋊C5 |
| unambiguous semidirect product | (C2×C3)⋊(C4×C11⋊C5) |
| unambiguous semidirect product | (C2×C11×Dic3)⋊C5 |
| derived, Hall | C3×C11 ⋊ C2×C4×C5 |
| Hall | C2×C11×Dic3 ⋊ C5 |
| Hall | C3×C11⋊C5 ⋊ C2×C4 |
| Sylow | C11 ⋊ C2×C5×Dic3 |
| Sylow | C3 ⋊ C2×C4×C11⋊C5 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D3×C11⋊C5, C2×(D33⋊C4)⋊C5, C2×Dic3×AGL(1,𝔽11), … |
| maximal normal subgroup of | C2×C4×D3×C11⋊C5, C2×(D33⋊C4)⋊C5, C2×Dic3×AGL(1,𝔽11), … |
| maximal quotient of | #208×C11⋊C5, #217×C11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1320, 31);