Finite Group DatabasebetaFinite Group Databasebeta| order | 10492 |
| isoclinism | isoclinic class of D43 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×Dic43 |
| unambiguous semidirect product | C43⋊(C4×C61) |
| derived, Sylow | C43 ⋊ C4×C61 |
| Hall | C43×C61 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C61 | D43 |
| commutator, hypocenter | C43 | C4×C61 |
| Frattini | C2 | C61×D43 |
| Fitting, socle, prime radical | C2×C43×C61 | C2 |
| cosocle | C2×C43 | C2×C61 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C61 | |
12 conjugacy classes of subgroups.
2806 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C61×Dic43, C61×Dic129, Dic43×C61⋊C3, … |
| maximal normal subgroup of | C3×C61×Dic43, Dic43×C61⋊C3, C61×(C43⋊C3)⋊C4, … |
| maximal quotient of | C3×C61×Dic43, C61×Dic129 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10492, 2);