Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C29 · Schur multiplier (H2) = C1 |
| direct product | C2×C29×#66524 |
| derived, Sylow | C37 ⋊ C2×C9×C29 |
| Hall | C2×C29×C37 ⋊ C9 |
| Hall | C29×C37 ⋊ C2×C9 |
| Hall | C2×C37 ⋊ C9×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C29 | C37⋊C3 |
| commutator, hypocenter | C37 | C2×C9×C29 |
| Frattini | C3 | C2×C29×C37⋊C3 |
| Fitting, socle, prime radical | C2×C3×C29×C37 | C3 |
| cosocle | C3×C37 | C2×C3×C29 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C3×C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19314 |
2610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C29×#66524, C29×#13050607, Dic29×#66524, … |
| maximal normal subgroup of | C4×C29×#66524, C29×#13050607, Dic29×#66524, … |
| maximal quotient of | C4×C29×#66524, C22×C29×#66524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 2);