Finite Group DatabasebetaFinite Group Databasebeta| order | 12212 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×Dic71 |
| unambiguous semidirect product | C71⋊(C4×C43) |
| derived, Sylow | C71 ⋊ C4×C43 |
| Hall | C43×C71 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D71 |
| commutator, hypocenter | C71 | C4×C43 |
| Frattini | C2 | C43×D71 |
| Fitting, socle, prime radical | C2×C43×C71 | C2 |
| cosocle | C2×C71 | C2×C43 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C43 | |
12 conjugacy classes of subgroups.
3182 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C43×Dic71, C43×Dic213, C43⋊C3×Dic71 |
| maximal normal subgroup of | C3×C43×Dic71, C43⋊C3×Dic71 |
| maximal quotient of | C3×C43×Dic71, C43×Dic213 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12212, 3);