Finite Group DatabasebetaFinite Group Databasebeta| order | 19012 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×C49×D97 |
| unambiguous semidirect product | C97⋊(C22×C49) |
| unambiguous semidirect product | (C2×C97)⋊(C2×C49) |
| Fitting | C2×C49×C97 ⋊ C2 |
| derived, Sylow | C97 ⋊ C22×C49 |
| Hall | C49×C97 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C49 | D97 |
| commutator, hypocenter | C97 | C22×C49 |
| Frattini | C7 | C2×C7×D97 |
| Fitting | C2×C49×C97 | C2 |
| socle | C2×C7×C97 | C2×C7 |
| prime radical | C2×C7×D97 | C7 |
| cosocle | C7×C97 | C22×C7 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C49 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9506 |
4900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19012, 11);