Finite Group DatabasebetaFinite Group Databasebeta| order | 10849 |
| automorphism | ? |
| homology | Abelianization (H1) = C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C571⋊C19 |
| Fitting, socle, derived, Sylow | C571 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C571 | C19 |
| LCS | G ▷ C571 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
19,571|b^a=b^40749 conjugacy classes — view the full character table.
| maximal subgroup of | D571⋊C19, C2×C571⋊C19, (C571⋊C3)⋊C19, … |
| maximal normal subgroup of | D571⋊C19, C2×C571⋊C19, (C571⋊C3)⋊C19, … |
| maximal quotient of | C2×C571⋊C19, C3×C571⋊C19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10849, 1);