Finite Group DatabasebetaFinite Group Databasebeta| order | 10348 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic199 |
| unambiguous semidirect product | C199⋊(C4×C13) |
| derived, Sylow | C199 ⋊ C4×C13 |
| Hall | C13×C199 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D199 |
| commutator, hypocenter | C199 | C4×C13 |
| Frattini | C2 | C13×D199 |
| Fitting, socle, prime radical | C2×C13×C199 | C2 |
| cosocle | C2×C199 | C2×C13 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C2×C13 | |
12 conjugacy classes of subgroups.
2626 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×Dic199, C13×Dic597, C13×(C199⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C13×Dic199, C13×(C199⋊C3)⋊C4, C13⋊C3×Dic199, … |
| maximal quotient of | C3×C13×Dic199, C13×Dic597 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10348, 3);