Finite Group DatabasebetaFinite Group Databasebeta| order | 5002 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D41 |
| unambiguous semidirect product | C41⋊(C2×C61) |
| Fitting, socle, Hall | C41×C61 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D41 |
| commutator, hypocenter | C41 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C41×C61 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C61 | |
8 conjugacy classes of subgroups.
1342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C61×D41, C61×D123, D41×C61⋊C3, … |
| maximal normal subgroup of | C3×C61×D41, D41×C61⋊C3, C5×C61×D41, … |
| maximal quotient of | C3×C61×D41, C61×D123, C5×C61×D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5002, 1);