Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C37 · Schur multiplier (H2) = C3 |
| direct product | C32×C37×D29 |
| unambiguous semidirect product | C29⋊(C2×C32×C37) |
| Fitting, socle, Hall | C32×C29×C37 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C32×C37 |
| Hall | C29×C37 ⋊ C2×C32 |
| Hall | C32×C29 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C37 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C32×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C37 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C32×C37 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9657 |
5328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C37×#1181, C32×#16864282, C32×D29×D37, … |
| maximal normal subgroup of | C32×C37×#1181, C32×#16864282, C32×D29×D37, … |
| maximal quotient of | C32×C37×Dic29, C2×C32×C37×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 35);