Finite Group DatabasebetaFinite Group Databasebeta| order | 990 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D55 |
| unambiguous semidirect product | C5⋊(C32×D11) |
| unambiguous semidirect product | C11⋊(C32×D5) |
| Fitting, socle, Hall | C32×C5×C11 ⋊ C2 |
| derived, Hall | C5×C11 ⋊ C2×C32 |
| Hall | C32×C11 ⋊ D5 |
| Hall | C32×C5 ⋊ D11 |
| Sylow | C11 ⋊ C32×D5 |
| Sylow | C5 ⋊ C32×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D55 |
| commutator, cosocle, hypocenter | C5×C11 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C11 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 495 |
261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D5×D11, C3×D3×D55, C3×D15⋊D11, … |
| maximal normal subgroup of | C32×D5×D11, C3×D3×D55, C3×D15⋊D11, … |
| maximal quotient of | C32×Dic55, C2×C32×D55, C32×D605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(990, 21);