Finite Group DatabasebetaFinite Group Databasebeta| order | 990 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C32×C11 ⋊ C2×C5 |
| derived | C3×C11 ⋊ C2×C3×C5 |
| Hall | C32×C11⋊C5 ⋊ C2 |
| Hall | C3×D33 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C3×D3 |
| Sylow | C11 ⋊ C3×C5×D3 |
| Sylow | C32 ⋊ AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C3×C11 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11 | C2×C5 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 66 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(990, 15);