Finite Group DatabasebetaFinite Group Databasebeta| order | 10749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3583⋊C3 |
| Fitting, socle, derived, Sylow | C3583 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3583 | C3 |
| LCS | G ▷ C3583 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
3,3583|b^a=b^10381197 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3583⋊C3, C2×C3583⋊C3, #44567477, … |
| maximal normal subgroup of | D3583⋊C3, C2×C3583⋊C3, #44567477, … |
| maximal quotient of | C2×C3583⋊C3, #44567475, C3×C3583⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10749, 1);