Finite Group DatabasebetaFinite Group Databasebeta| order | 10004 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D61 |
| unambiguous semidirect product | (C61×D41)⋊C2 |
| unambiguous semidirect product | (C41×D61)⋊C2 |
| unambiguous semidirect product | D2501⋊C2 |
| Fitting, socle, derived, Hall | C41×C61 ⋊ C22 |
| Sylow | C61 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C61 | C22 |
| LCS | G ▷ C41×C61 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
704 conjugacy classes — view the full character table.
| maximal subgroup of | D41×D61⋊C3, C3×D41×D61, D61×D123, … |
| maximal normal subgroup of | D41×D61⋊C3, C3×D41×D61 |
| maximal quotient of | C3×D41×D61, D61×D123, D41×D183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10004, 12);