Finite Group DatabasebetaFinite Group Databasebeta| order | 19908 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic79⋊C9 |
| unambiguous semidirect product | Dic79⋊(C7×C9) |
| unambiguous semidirect product | (C79⋊C9)⋊(C4×C7) |
| derived, Sylow | C79 ⋊ C4×C7×C9 |
| Hall | C7×C79⋊C9 ⋊ C4 |
| Hall | C7×Dic79 ⋊ C9 |
| Hall | C79⋊C9 ⋊ C4×C7 |
| Hall | C7×C79 ⋊ C4×C9 |
| Hall | Dic79 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D79⋊C3 |
| commutator, hypocenter | C79 | C4×C7×C9 |
| Frattini | C2×C3 | C7×D79⋊C3 |
| Fitting, socle, prime radical | C2×C3×C7×C79 | C2×C3 |
| cosocle | C2×C3×C79 | C2×C3×C7 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C3×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19908 |
798 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19908, 13);