Finite Group DatabasebetaFinite Group Databasebeta| order | 10004 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C61 · Schur multiplier (H2) = C2 |
| direct product | C2×C61×D41 |
| unambiguous semidirect product | C41⋊(C22×C61) |
| unambiguous semidirect product | (C2×C41)⋊(C2×C61) |
| Fitting, socle | C2×C41×C61 ⋊ C2 |
| derived, Sylow | C41 ⋊ C22×C61 |
| Hall | C41×C61 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C61 | D41 |
| commutator, cosocle, hypocenter | C41 | C22×C61 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41×C61 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C61 | |
20 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D41×C61⋊C3, D3×C61×D41, C2×C3×C61×D41, … |
| maximal normal subgroup of | C2×D41×C61⋊C3, C2×C3×C61×D41 |
| maximal quotient of | D3×C61×D41, C2×C3×C61×D41, C2×C61×D123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10004, 14);