Finite Group DatabasebetaFinite Group Databasebeta| order | 9918 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C29 · Schur multiplier (H2) = C3 |
| direct product | C32×C29×D19 |
| Fitting, socle, Hall | C32×C19×C29 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C32×C29 |
| Hall | C19×C29 ⋊ C2×C32 |
| Hall | C32×C19 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C29 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C32×C29 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C29 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C32×C29 | |
48 conjugacy classes of subgroups.
2871 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D19×D29, C3×D3×C29×D19, C3×D19×D87, … |
| maximal normal subgroup of | C32×D19×D29, C3×D3×C29×D19, C3×D19×D87, … |
| maximal quotient of | C32×C29×Dic19, C2×C32×C29×D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9918, 27);