Finite Group DatabasebetaFinite Group Databasebeta| order | 19691 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×C29⋊C7 |
| unambiguous semidirect product | C29⋊(C7×C97) |
| unambiguous semidirect product | (C29×C97)⋊C7 |
| Fitting, socle, Hall | C29×C97 ⋊ C7 |
| derived, Sylow | C29 ⋊ C7×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C7×C97 |
| Frattini | C1 | G |
| Fitting, socle | C29×C97 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C97 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2813 |
1067 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19691, 1);