Finite Group DatabasebetaFinite Group Databasebeta| order | 10339 |
| automorphism | ? |
| homology | Abelianization (H1) = C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C211⋊C49 |
| derived, Sylow | C211 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | C211⋊C7 |
| commutator, hypocenter | C211 | C49 |
| Fitting, socle, prime radical, cosocle | C7×C211 | C7 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C7 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
7^2,211|a^7=b,c^a=c^171259 conjugacy classes — view the full character table.
| maximal subgroup of | D211⋊C49, C2×C211⋊C49, (C211⋊C3)⋊C49, … |
| maximal normal subgroup of | D211⋊C49, C2×C211⋊C49, (C211⋊C3)⋊C49, … |
| maximal quotient of | C2×C211⋊C49, C3×C211⋊C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10339, 1);