Finite Group DatabasebetaFinite Group Databasebeta| order | 19071 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#13091812 |
| derived, Sylow | C163 ⋊ C9×C13 |
| Hall | C13×C163 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C163⋊C3 |
| commutator, hypocenter | C163 | C9×C13 |
| Frattini | C3 | C13×C163⋊C3 |
| Fitting, socle, prime radical | C3×C13×C163 | C3 |
| cosocle | C3×C163 | C3×C13 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C3×C13 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19071 |
2223 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C13×#13091812, C13×#13091812⋊C2, D13×#13091812, … |
| maximal normal subgroup of | C2×C13×#13091812, C13×#13091812⋊C2, D13×#13091812, … |
| maximal quotient of | C2×C13×#13091812 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19071, 3);