Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of C3⋊(C3⋊AGL(1,𝔽11)) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊(C3⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C2×C11⋊C5)⋊(C3⋊D3) |
| unambiguous semidirect product | (C2×C3⋊D33)⋊C5 |
| Fitting, socle | C2×C32×C11 ⋊ C2×C5 |
| derived, Hall | C32×C11 ⋊ C22×C5 |
| Hall | C32×C11⋊C5 ⋊ C22 |
| Hall | C2×C3⋊D33 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C3⋊D3 |
| Sylow | C11 ⋊ C2×C5×C3⋊D3 |
| Sylow | C32 ⋊ C2×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C3⋊AGL(1,𝔽11)) |
| commutator, cosocle, hypocenter | C32×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C11 | C2×C5 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 71);