Finite Group DatabasebetaFinite Group Databasebeta| order | 19282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C2×C311⋊C31 |
| unambiguous semidirect product | (C2×C311)⋊C31 |
| Fitting, socle, Hall | C2×C311 ⋊ C31 |
| derived, Sylow | C311 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C311⋊C31 |
| commutator, cosocle, hypocenter | C311 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C311 | C31 |
| LCS | G ▷ C311 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 622 |
82 conjugacy classes — view the full character table.
| maximal subgroup of | Dic311⋊C31, C4×C311⋊C31, C2×D311⋊C31, … |
| maximal normal subgroup of | Dic311⋊C31, C4×C311⋊C31, C2×D311⋊C31, … |
| maximal quotient of | C4×C311⋊C31, C22×C311⋊C31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19282, 2);