Finite Group DatabasebetaFinite Group Databasebeta| order | 10230 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C3⋊AGL(1,𝔽11) |
| unambiguous semidirect product | C3⋊(C31×AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊(D3×C31) |
| unambiguous semidirect product | D33⋊(C5×C31) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C3⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C11 | C2×C5×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C31 | C2×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C31 | |
32 conjugacy classes of subgroups.
558 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10230, 61);