Finite Group DatabasebetaFinite Group Databasebeta| order | 12212 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C71 · Schur multiplier (H2) = C2 |
| direct product | C2×C71×D43 |
| unambiguous semidirect product | C43⋊(C22×C71) |
| unambiguous semidirect product | (C2×C43)⋊(C2×C71) |
| Fitting, socle | C2×C43×C71 ⋊ C2 |
| derived, Sylow | C43 ⋊ C22×C71 |
| Hall | C43×C71 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C71 | D43 |
| commutator, cosocle, hypocenter | C43 | C22×C71 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43×C71 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C71 | |
20 conjugacy classes of subgroups.
3266 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C71×D43⋊C3, D3×C71×D43, C2×C3×C71×D43, … |
| maximal normal subgroup of | C2×C71×D43⋊C3, C2×C3×C71×D43 |
| maximal quotient of | D3×C71×D43, C2×C3×C71×D43, C2×C71×D129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12212, 8);