Finite Group DatabasebetaFinite Group Databasebeta| order | 19124 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic683 |
| unambiguous semidirect product | C683⋊(C4×C7) |
| derived, Sylow | C683 ⋊ C4×C7 |
| Hall | C7×C683 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D683 |
| commutator, hypocenter | C683 | C4×C7 |
| Frattini | C2 | C7×D683 |
| Fitting, socle, prime radical | C2×C7×C683 | C2 |
| cosocle | C2×C683 | C2×C7 |
| LCS | G ▷ C683 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19124 |
4802 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19124, 3);