Finite Group DatabasebetaFinite Group Databasebeta| order | 12214 |
| isoclinism | isoclinic class of D197 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D197 |
| unambiguous semidirect product | C197⋊(C2×C31) |
| Fitting, socle, Hall | C31×C197 ⋊ C2 |
| derived, Sylow | C197 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D197 |
| commutator, cosocle, hypocenter | C197 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C197 | C2 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
3100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#11716161, C31⋊#11716161, D31×D197, … |
| maximal normal subgroup of | C31×#11716161, C31⋊#11716161, D31×D197, … |
| maximal quotient of | C31×Dic197, C2×C31×D197, C3×C31×D197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12214, 2);