Finite Group DatabasebetaFinite Group Databasebeta| order | 660 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C2×C3)⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C2×C11⋊C5)⋊D3 |
| unambiguous semidirect product | (C2×D33)⋊C5 |
| Fitting, socle | C2×C3×C11 ⋊ C2×C5 |
| derived, Hall | C3×C11 ⋊ C22×C5 |
| Hall | C3×C11⋊C5 ⋊ C22 |
| Hall | C2×D33 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×D3 |
| Sylow | C11 ⋊ C2×C5×D3 |
| Sylow | C3 ⋊ C2×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C11 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C11 | C2×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 66 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | (D33⋊C4)⋊C5, #63141⋊C5, #63142⋊C5, … |
| maximal normal subgroup of | (D33⋊C4)⋊C5, #63141⋊C5, #63142⋊C5, … |
| maximal quotient of | Dic66⋊C5, C4×C3⋊AGL(1,𝔽11), C4⋊(C3⋊AGL(1,𝔽11)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(660, 19);