Finite Group DatabasebetaFinite Group Databasebeta| order | 12218 |
| isoclinism | isoclinic class of D149 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D149 |
| unambiguous semidirect product | C149⋊(C2×C41) |
| Fitting, socle, Hall | C41×C149 ⋊ C2 |
| derived, Sylow | C149 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D149 |
| commutator, cosocle, hypocenter | C149 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C149 | C2 |
| LCS | G ▷ C149 | |
| UCS | C1 ◁ C41 | |
8 conjugacy classes of subgroups.
3116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#10597010, #37567715, D41×D149, … |
| maximal normal subgroup of | C41×#10597010, #37567715, D41×D149, … |
| maximal quotient of | C41×Dic149, C2×C41×D149, C3×C41×D149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12218, 2);