Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C29 · Schur multiplier (H2) = C3 |
| direct product | C32×C29×D37 |
| Fitting, socle, Hall | C32×C29×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C32×C29 |
| Hall | C29×C37 ⋊ C2×C32 |
| Hall | C32×C37 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C29 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C32×C29 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32×C29 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9657 |
5220 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C29×#3866, C32×#16864283, C32×D29×D37, … |
| maximal normal subgroup of | C32×C29×#3866, C32×#16864283, C32×D29×D37, … |
| maximal quotient of | C32×C29×Dic37, C2×C32×C29×D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 36);